2021
18
2
0
148
1

Coincidence Point Results for Different Types of $ H_b^{+} $contractions on $m_b$Metric Spaces
https://scma.maragheh.ac.ir/article_244075.html
10.22130/scma.2020.131553.836
1
In this paper, we give some properties of $m_b$metric topology and prove Cantor's intersection theorem in $m_b$metric spaces. Moreover, we introduce some newclasses of $H_b^+ $contractions for a pair of multivalued and singlevalued mappings and discuss their coincidence points. Some examples are provided to justify the validity of our main results.
0

1
31


Sushanta
Mohanta
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata700126, West Bengal, India.
India
mohantawbsu@rediffmail.com


Shilpa
Patra
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata700126, West Bengal, India.
India
shilpapatrabarasat@gmail.com
$m_b$metric
$m_b$Cauchy sequence
$H_b^+ $contraction
Coincidence point
[[1] S.M.A. Aleomraninejad, Sh. Rezapour and N. Shahzad, Convergence of an iterative scheme for multifunctions, J. Fixed Point Theory Appl., 12 (2012), pp. 239246.##[2] S.M.A. Aleomraninejad, Sh. Rezapour and N. Shahzad, Fixed points of hemiconvex multifunctions, Topo. Metd. Nonlinear Anal., 37 (2011), pp. 383389.##[3] S.M.A. Aleomraninejad and N. Shahzad, On fixed point generalizations of Suzuki's method, Appl. Math. Lett., 24 (2011), pp. 10371040.##[4] S.M.A. Aleomraninejad and N. Shahzad, Some fixed point results on a metric space with a graph, Topo. Appl., 159 (2012), pp. 659663.##[5] M. Asadi, E. Karapinar and P. Salimi, New extension of $p$metric spaces with some fixedpoint results on $M$metric spaces, J. Inequal. Appl., 2014 (2014), pp. 19.##[6] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal.,Gos. Ped. Inst. Unianowsk, 30 (1989), pp. 2637.##[7] I. Beg and A. Azam, Fixed points of multivalued locally contractive mappings, Boll. Unione Matematica Italiana, 7 (1990), pp. 227233.##[8] I. Beg and A.R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods and Appl., 71 (2009), pp. 36993704.##[9] S. Czerwik, Contraction mappings in $b$metric spaces, Acta Math. Inform. Univ. Ostrav, 1 (1993), pp. 511.##[10]B. Damjanovic, B. Samet and C. Vetro, Common fixed point theorems for multivalued maps, Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), pp. 818824.##[11] R.H. Haghi and Sh. Rezapour, Fixed points of multifunctions on regular cone metric spaces, Expositiones Mathematicae, 28 (2010), pp. 7177.##[12] R.H. Haghi, Sh. Rezapour and N. Shahzad, Be caraful on partial metric fixed point results, Topo. Appl., 160 (2013), pp. 450454.##[13] R.H. Haghi, Sh. Rezapour and N. Shahzad, On fixed points of quasicontraction type multifunctions, Appl. Math. Lett., 25(5) (2012), pp. 843846.##[14] R.H. Haghi, Sh. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Analysis: Theory, Methods and Appl., 74(5) (2011), pp. 17991803.##[15] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), pp. 14681476.##[16] E. Karapinar, A note on common fixed point theorems in partial metric spaces, Miskolc Math. Notes, 12 (2011), pp. 185191.##[17] E. Karapinar, Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl., 2011 (2011), pp. 17.##[18] E. Karapinar and S. Romaguera, Nonunique fixed point theorems in partial metric spaces, Filomat, 27 (2013), pp. 13051314.##[19] Z. Ma and L. Jiang, $C^*$algebravalued $b$metric spaces and related fixed point theorems, Fixed Point Theory Appl., 2015 (2015), pp. 112.##[20] Z. Ma, L. Jiang and H. Sun, $C^*$algebravalued metric spaces and related fixed point theorems, Fixed Point Theory Appl., 2014 (2014), pp. 111.##[21] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci., 728 (1994), pp. 183197.##[22] S.K. Mohanta and S. Mohanta, A common fixed point theorem in $G$metric spaces, Cubo, A Mathematical Journal, 14 (2012), pp. 85101.##[23] S.K. Mohanta and S. Mohanta, Some fixed point results for mappings in $G$metric spaces, Demonstratio Mathematica, 47 (2014), pp. 179191.##[24] S.K. Mohanta and S. Patra, Coincidence points and common fixed points for hybrid pair of mappings in $b$metric spaces endowed with a graph, J. Linear. Topological. Algebra., 6 (2017), pp. 301321.##[25] Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete $G$metric spaces, Fixed Point Theory Appl., 2009 (2009), pp. 110.##[26] S.B. Nadler, Multivalued contraction mappings, Pacific J. Math., 30 (1969), pp. 475488.##[27] Sh. Rezapour and R.H. Haghi, Two results about fixed point of multifunctions, Bull. Iranian Math. Soc., 36 (2010), pp. 279287.##[28] Sh. Rezapour, R.H. Haghi and N. Shahzad, Some notes on fixed points of quasicontraction maps, Appl. Math. Lett., 23 (2010), pp. 498502.##[29] H. Sahin, I. Altun and D. Turkoglu, Fixed point results for mixed multivalued mappings of FengLiu type on $M_b$metric spaces, Mathematical Methods in Engineering, Nonlinear Systems and Complexity, 23 (2019), pp. 6780.##]
1

Joint Continuity of Bimultiplicative Functionals
https://scma.maragheh.ac.ir/article_240861.html
10.22130/scma.2020.127223.795
1
For Banach algebras $mathcal{A}$ and $mathcal{B}$, we show that if $mathfrak{A}=mathcal{A}times mathcal{B}$ is unital, then each bimultiplicative mapping from $mathfrak{A}$ into a semisimple commutative Banach algebra $mathcal{D}$ is jointly continuous. This conclusion generalizes a famous result due to$check{text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$bimultiplicative functionals on $mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$.
0

33
44


Abbas
ZivariKazempour
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
Iran
zivari6526@gmail.com


Mohamad
Valaei
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
Iran
mohamad.valaei@abru.ac.ir
Jointly continuous
Bimultiplicative functional
Almost bimultiplicative
[[1] J.F. Berglund, H.D. Junghenn and P. Milnes, Analysis on Semigroups, JohnWiley, New York, 1989.##[2] F.F. Bonsall and J. Duncan, Complete normed algebra, SpringerVerlag, New York, 1973.##[3] J. Bracic and M. S. Moslehian, On automatic continuity of $3$homomorphisms on Banach algebras, Bull. Malay. Math. Sci. Soc., 30(2) (2007), pp. 195200.##[4] H.G. Dales, Banach Algebras and Automatic Continuity, Vol. 24 London Mathematical Society Monographs, Clarendon Press, Oxford, 2000.##[5] M. Eshaghi Gordji, A. Jabbari and E. Karapinar, Automatic continuity of surjective $n$homomorphisms on Banach algebras, Bull. Iranian Math. Soc., 41(5) (2015), pp. 12071211.##[6] Sh. Hejazian, M. Mirzavaziri and M.S. Moslehian, $n$homomorphisms, Bull. Iranian Math. Soc., 31(1) (2005), pp. 1323.##[7] T.G. Honari and H. Shayanpour, Automatic continuity of $n$homomorphisms between Banach algebras, Q. Math., 33(2) (2010), pp. 189196.##[8] K. Jarosz, Perturbation of Banach algebras, Lecture Notes in Mathematics, Springerverlag, 1985.##[9] B.E. Johnson, Approximately multiplicative functionals, J. London Math. Soc., 34(2) (1986), pp. 489510.##[10] B.E. Johnson, Approximately multiplicative maps between Banach algebras, J. London Math. Soc., 37(2) (1988), pp. 294316.##[11] W. Rudin, Functional Analysis, McGrawHill, New York, 1973.##[12] A. Zivarikazempour, A characterization of $3$Jordan homomorphisms on Banach algebras, Bull. Aust. Math. Soc., 93(2) (2016), pp. 301306.##[13] A. ZivariKazempour, When is a biJordan homomorphisms bihomomorphisms?, Kragujevac J. Math., 42(4) (2018), pp. 485493.##]
1

Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}left( sright) $Metric Spaces
https://scma.maragheh.ac.ir/article_242300.html
10.22130/scma.2020.127414.799
1
In this paper, necessary and sufficient conditions for the existence and uniqueness of fixed points of generalized Geraghty type contraction mappings are given in complete partial $b_{v}(s) $metric spaces. The results are more general than several results that exist in the literature because of the considered space. A numerical example is given to support the obtained results. Also, the existence and uniqueness of the solutions of an integral equation has been verified considered as an application.
0

45
62


Ebru
Altiparmak
Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.
Turkey
ebru.altiparmak@erzurum.edu.tr


Ibrahim
Karahan
Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.
Turkey
ibrahimkarahan@erzurum.edu.tr
Generalized Geraghty contraction
Fixed point
Partial $b_{v}left( sright) $ metric spaces
Generalized metric space
[[1] M.S. Abdullahi and P. Kumam, Partial $b_{v(s)} $metric spaces and fixed point theorems, J. Fixed Point Theory Appl., 20 (2018), 13 pages.##[2] O. Acar and I. Altun, A fixed point theorem for $ F$Geraghty contraction on metriclike spaces, Fasc. Math., 59 (2017), pp. 512.##[3] H. Afshari, H. Alsulami and E. Karapinar, On the extended multivalued Geraghty type contractions, J. Nonlinear Sci. Appl., 9 (2016), pp. 46954706.##[4] S. Aleksic, Z.D. Mitrovic and S. Radenovic, A fixed point theorem of Jungck in $b_{v(s)}$metric spaces, Period. Math. Hungar., 77 (2018), pp. 224231.##[5] B. Alqahtani, A. Fulga and E. Karapinar, A short note on the common fixed points of the Geraghty contraction of type $E_{S,T}$, Demonstr. Math., 51 (2018), pp. 233240.##[6] I. Altun and K. Sadarangani, Generalized Geraghty type mappings on partial metric spaces and fixed point results, Arab J. Math., 2 (2013), pp. 247253.##[7] M. Arshad and A. Hussain, Fixed point results for generalized rational $alpha $Geragty contraction, Miskolc Math. Notes, 18 (2017), pp. 611621.##[8] H. Aydi, A. Felhi and H. Afshari, New Geraghty type contractions on metriclike spaces, J. Nonlinear Sci. Appl., 10 (2017), pp. 780788.##[9] S. Chandok, Some fixed point theorems for $( alpha ,beta ) $admissible Geraghty type contractive mappings and related results, Math. Sci., 9 (2015), pp. 127135.##[10] A.K. Dubey, U. Mishra and W.H. Lim, Some new fixed point theorems for generalized contractions involving rational expressions in complex valued $b$metric spaces, Nonlinear Funct. Anal. Appl., 24 (2019), pp. 477483.##[11] D. Dukic, Z. Kadelburg and S. Radenovic, Fixed Points of GeraghtyType Mappings in Various Generalized Metric Spaces, Abstr. Appl. Anal., 2011 (2011), 13 pages.##[12] O. Ege, Complex valued rectangular bmetric spaces and an application to linear equations, J. Nonlinear Sci. Appl., 8 (2015), pp. 10141021 .##[13] I.M. Erhan, Geraghty type contraction mappings on Branciari $b$metric spaces, Adv. Theory Analysis Appl., 1 (2017), pp. 147160.##[14] H. Faraji, D. Savic and S. Radenovic, Fixed point theorems for Geraghty type mappings in $b$metric spaces and Applications, Axioms, 8 (2019), 12 pages.##[15] M.A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), pp. 604608.##[16] M.E. Gordji, H. Baghani, H. Khodaei and M. Ramezani, Geraghty's fixed point theorem for special Multivalued mappings, Thai J. Math., 10 (2010), pp. 225231.##[17] H. Huang, L. Paunovic and S. Radenovic, On some new fixed point results for rational Geraghty contractive mappings in ordered bmetric spaces, J. Inequal. Appl., 8 (2015), pp. 800807.##[18] A. Hussain, Modified Geraghty contraction involving fixed point theorems, Jordan J. Math. Stat., 10 (2017), pp. 95112.##[19] M. Jovanovic, Z. Kadelburg and S. Radenovic, Common fixed point results in metrictype spaces, Fixed Point Theory Appl., 2010 (2010), 15 pages.##[20] Z. Kadelburg and P. Kumam, S. Radenovic and W. Sintunavarat, Common coupled fixed point theorems for Geraghtytype contraction mappings using monotone property, Fixed Point Theory Appl., 2015 (2015), 14 pages.##[21] I. Karahan and I. Isik, Partial $b_{v( s)} $ , Partial $v$generalized and $b_{v( theta )} $ metric spaces and related fixed point theorems, Facta Univ. Ser. Math. Inform., (In Press).##[22] E. Karapinar, On best proximity point of $psi $ Geraghty contractions, Fixed Point Theory Appl., 2013 (2013), 9 pages.##[23] E. Karapinar, $alpha $$psi $Geraghty contraction type mappings and some related fixed point results, Filomat, 28 (2014), pp. 3748.##[24] E. Karapinar and B. Samet, A note on '$psi $Geraghty type contractions', Fixed Point Theory Appl., 2014 (2014), 5 pages.##[25] Z.D. Mitrovic, H. Aydi, Z. Kadelburg and G.S. Rad, On some rational contractions in $b_{v( s)} $metric spaces, Rend. Circ. Mat. Palermo 2 (2019), 11 pages.##[26] Z.D. Mitrovic, H. Aydi and S. Radenovic, On Banach and Kannan type results in cone $b_{v( s)} $metric spaces over Banach algebra, Acta Math. Univ. Comenian., LXXXIX (2020), pp. 143152.##[27] Z.D. Mitrovic and S. Radenovic, The Banach and Reich contractions in $b_{v( s)} $metric spaces, J. Fixed Point Theory Appl., 19 (2017), pp. 30873095.##[28] Z. Mostefaoui, M. Bousselsal and J.K. Kim, Some results in fixed point theory concerning rectangular bmetric spaces, Nonlinear Funct. Anal. Appl., 24 (2019), pp. 4959.##[29] Y.J. Piao, Fixed point theorems for contractive and expansive mappings of Geraghty type on $2$metric spaces, Adv. Fixed Point Theory, 6 (2016), pp. 123135.##[30] K.N.V.V. Vara Prasad and A.K. Singh, Fixed point results for rational $alpha $Geraghty contractive mappings, Adv. Inequal. Appl., 2019 (2019), 15 pages.##[31] V.L. Rosa and P. Vetro, Fixed points for Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl., 7 (2014), pp. 110.##[32] R.J. Shahkoohi and A. Razani, Some fixed point theorems for rational Geraghty contractive mappings in ordered $b$metric spaces, J. Inequal. Appl., 2014 (2014), 23 pages.##[33] A.Wiriyapongsanon and N. Phudolsitthiphat, Coincidence point theorems for Geraghtytype contraction mappings in generalized metric spaces, Thai J. Math., (2018), pp. 145158.##]
1

Some Properties of Complete Boolean Algebras
https://scma.maragheh.ac.ir/article_242304.html
10.22130/scma.2020.127693.802
1
The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all realvalued continuous functions and the equivalence classes of $lambda$measurable. We shall provide conditions which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice and $(B,, sigma)$ is a Hausdorff space and $B$ satisfies the $G_sigma$ property, then $B$ carries a strictly positive Maharam submeasure.
0

63
71


Ali
Molkhasi
Department of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.
Iran
molkhasi@gmail.com
$q^prime$compactness
Strongly algebraically closed algebras
Complete Boolean algebras
[[1] B. Balcar, T. Jech and T. Pazak, Complete ccc Booleab algebras, the order sequential topology, and a problem of Von Neumann, Bull. London Math. Soc., 37 (2005), pp. 885898.##[2] E. Behrends, $L^p$Struktur in Banachraumen, Studia Math., 55 (1976), pp. 7185.##[3] G. Birkhoff, Lattice theory, Colloq. Publ., Vol. 25, Amer. Math. Soc, Providence, R. I., 1967.##[4] F. Cunningham, $L$structure in $L$spaces, Trans. Amer. Math. Soc., 95 (1960), pp. 274299.##[5] E. Daniyarova, A. Miasnikov, and V. Remeslennikov, Unification theorems in algebraic geometry, Algebra and Discrete Mathematics, 1 (2008), pp. 80112.##[6] S. Givant and P. Halmos, Introduction to Boolean algebras, Springer Science$+$ Business Media, New York, 2009.##[7] V.A. Gorbunov, Algebraic theory of quasivarieties, Nauchnaya Kniga, Novosibirsk, 1999; English transl., Plenum, 1998.##[8] G. Gratzer, Universal algebra, Van Nostrand, Princeton, N. J., 2008.##[9] G. Higman and E.L. Scott, Existentially Closed Groups, Clarendon Press, 1988.##[10] W. Hodges, Model theory, University Press, Cambridge, 1993.##[11] A.G. Kusraev and S.S. Kutateladze, Nonstandard Methods of Analysis [in Russian], Nauka, Novosibirsk (1990).##[12] D. Maharam, An algebraic characterization of measure algebras, Ann. of Math., 48 (1947), pp. 154167.##[13] A. Molkhasi, On strrongly algebraically closed lattices, J. Sib. Fed. Univ. Math. Phys., 9 (2016), pp. 202208.##[14] A. Myasnikov and V. Remeslennikov, Algebraic geometry over groups II: logical foundations, J. Algebra, 234 (2000), pp. 225276.##[15] B. Plotkin, Algebras with the same (algebraic) geometry, Proc. Steklov Inst. Math., 242 (2003), pp. 165196.##[16] J. Schmid, Algebraically and existentially closed distributive lattices, Zeilschr f. miath. Logik und Crztndlagen d. Math. Bd., 25 (1979), pp. 525530.##[17] W.R. Scott, Algebraically closed groups, Proc. Amer. Math. Soc., 2 (1951), pp. 118121.##[18] A. Shevlyakov, Algebraic geometry over Boolean algebras in the language with constants, J. Math. Sciences, 206 (2015), pp. 724757.##[19] R. Sikorski, Boolean Algebras, SpringerVerlag, Berlin etc., 1964.##[20] D.A. Vladimirov, Boolean algebras, Nauka, Moscow, 1969.##]
1

Second Module Cohomology Group of Induced Semigroup Algebras
https://scma.maragheh.ac.ir/article_242308.html
10.22130/scma.2020.130935.826
1
For a discrete semigroup $ S $ and a left multiplier operator $T$ on $S$, there is a new induced semigroup $S_{T}$, related to $S$ and $T$. In this paper, we show that if $T$ is multiplier and bijective, then the second module cohomology groups $mathcal{H}_{ell^1(E)}^{2}(ell^1(S), ell^{infty}(S))$ and $mathcal{H}_{ell^1(E_{T})}^{2}(ell^1({S_{T}}), ell^{infty}(S_{T}))$ are equal, where $E$ and $E_{T}$ are subsemigroups of idempotent elements in $S$ and $S_{T}$, respectively. Finally, we show thet, for every odd $ninmathbb{N}$, $mathcal{H}_{ell^1(E_{T})}^{2}(ell^1(S_{T}),ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.
0

73
84


Mohammad Reza
Miri
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
Iran
mrmiri@birjand.ac.ir


Ebrahim
Nasrabadi
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
Iran
nasrabadi@birjand.ac.ir


Kianoush
Kazemi
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
Iran
kianoush.kazemi@birjand.ac.ir
second module cohomology group
inverse semigroup
induced semigroup
semigroup algebra
[[1] M. Amini, Module amenability fore semigroup algebra, Semigroup Forum., 69 (2004), pp. 243254.##[2] M. Amini and D.E. Bagha, Weak module amenability fore semigroup algebra, Semigroup Forum., 71 (2005), pp. 1826.##[3] F.T. Birtel, Banach algebra of multiplier, Duke Math. J, 28 (1961), pp. 203211.##[4] J. Laali, The multipliers related products in Banach algebras, Quaestion Mathematicae., 37 (2014), pp. 117.##[5] R. Larsen, An introduction to the theory of multipliers, Springerverlag, New York., (1971).##[6] E. Nasrabadi, First and second module cohomology groups for non commutative semigroup algebras, Sahand Commun. Math. Anal., 17 (2020), pp. 3947.##[7] E. Nasrabadi and A. Pourabbas, Module cohomology group of inverse semigroup algebra, Bulletin of Iranian Mathematical Society., 37 (2011), pp. 157169.##[8] E. Nasrabadi and A. Pourabbas, Second module cohomology group of inverse semigroup algebra, Semigroup Fourm., 81 (2010), pp. 269278.##[9] A.L. Paterson, Amenability, American Mathematical Society, (1988).##[10] M.H. Sattari and H. Shafieasl, Symmetric module and Connes amenability, Sahand Commun. Math. Anal., 5 (2017), pp. 4959.##]
1

Two Equal Range Operators on Hilbert $C^*$modules
https://scma.maragheh.ac.ir/article_242934.html
10.22130/scma.2020.130093.821
1
In this paper, number of properties, involving invertibility, existence of MoorePenrose inverse and etc for modular operators with the same ranges on Hilbert $C^*$modules are presented. Natural decompositions of operators with closed range enable us to find some relations of the product of operators with MoorePenrose inverses under the condition that they have the same ranges in Hilbert $C^*$modules. The triple reverse order law and the mixed reverse order law in the special cases are also given. Moreover, the range property and MoorePenrose inverse are illustrated.
0

85
96


Ali Reza
Janfada
Department of Mathematics, Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Iran.
Iran
ajanfada@birjand.ac.ir


Javad
FarokhiOstad
Department of Basic sciences, Birjand University of Technology, Birjand 9719866981, Iran.
Iran
javadfarrokhi90@gmail.com
Closed range
MoorePenrose inverse
Hilbert $C^*$module
[[1] R. Bouldin, Closed range and relative regularity for products, J. Math. Anal. Appl., 61, (1977), pp. 397403.##[2] R. Bouldin, The product of operators with closed range, Tohoku Math. J., 25(2), (1973), pp. 359363.##[3] C.Y. Deng and H.K. Du, Representations of the MoorePenrose inverse for a class of 2 by 2 block operator valued partial matrices, Linear Multilinear Algebra, 58, (2010), pp. 1526.##[4] D.S. Djordjevic, Further results on the reverse order law for generalized inverses, SIAM J. Matrix Anal. Appl., 29(4), (2007), pp. 12421246.##[5] J. FarokhiOstad and A.R. Janfada, Products of EP operators on Hilbert $C^*$Modules, Sahand Commun. Math. Anal., 10, (2018), pp. 6171.##[6] J. FarokhiOstad and A.R. Janfada, On closed range $C^*$modular operators, Aust. J. Math. Anal. Appl., 15(2), (2018), pp. 19.##[7] S. Izumino, The product of operators with closed range and an extension of the reverse order law, Tohoku Math. J., 34(2), (1982), pp. 4352.##[8] M. Jalaeian, M. Mohammadzadeh Karizaki and M. Hassani, Conditions that the product of operators is an EP operator in Hilbert $C^*$module, Linear Multilinear Algebra, 68(10), (2020), pp. 19902004.##[9] E.C. Lance, Hilbert $C^*$Modules, LMS Lecture Note Series 210, Cambridge Univ. Press, 1995.##[10] M. Mohammadzadeh Karizaki, Antisymmetric relations of operators which satisfy specified conditions, Funct. Anal. Approx. Comput., 10(3), (2018), pp. 1520##[11] M. Mohammadzadeh Karizaki and D.S. Djordjevic, Commuting $C^*$ modular operators, Aequationes mathematicae, 90(6), pp. 11031114.##[12] M. Mohammadzadeh Karizaki, M. Hassani and M. Amyari, MoorePenrose inverse of product operators in Hilbert $C^*$modules, Filomat, 30(13), (2016), pp. 33973402.##[13] M. Mohammadzadeh Karizaki, M. Hassani, M. Amyari and M. Khosravi, Operator matrix of MoorePenrose inverse operators on Hilbert $C^*$modules, Colloq. Math., 140, (2015), pp. 171182.##[14] M.S. Moslehian, K. Sharifi, M. Forough and M. Chakoshi, MoorePenrose inverse of Gram operator on Hilbert $C^*$modules, Studia Math., 210(2), (2012), 189196.##[15] G.J. Murphy, $C^*$algebras and operator theory, Academic Press Inc., Boston, MA, 1990.##[16] Z. Niazi Moghani, M. Khanehgir and M. Mohammadzadeh Karizaki, Explicit solution to the operator equation $AXD + FX^*B = C$ over Hilbert $C^*$modules, J. Math. Anal. Appl., 10(1), (2019), pp. 5264.##[17] K. Sharifi, EP modular operators and their products, J. Math. Anal. Appl., 419, (2014), pp. 870877.##[18] K. Sharifi, The product of operators with closed range in Hilbert $C^*$modules, Linear Algebra Appl., 435, (2011), pp. 11221130.##[19] K. Sharifi and B. Ahmadi Bonakdar, The reverse order law for MoorePenrose inverses of operators on Hilbert $C^*$modules, Bull. Iran. Math. Soc., 42(1), (2016), pp. 5360.##[20] M. Vosough and M.S. Moslehian, Operator and Matrix Equations, Ph.d thesis, Ferdowsi University of Mashhad, (2017).##[21] M. Vosough and M.S. Moslehian, Solutions of the system of operator equations $BXA=B=AXB=AXB$ via $*$order, Electron. J. Linear Algebra, 32, (2017), pp. 172183.##[22] Q. Xu and L. Sheng, Positive semidefinite matrices of adjointable operators on Hilbert $C^*$modules, Linear Algebra Appl., 428, (2008), pp. 9921000.##]
1

Using Frames in Steepest DescentBased Iteration Method for Solving Operator Equations
https://scma.maragheh.ac.ir/article_244071.html
10.22130/scma.2020.123786.771
1
In this paper, by using the concept of frames, two iterative methods are constructed to solve the operator equation $ Lu=f $ where $ L:Hrightarrow H $ is a bounded, invertible and selfadjoint linear operator on a separable Hilbert space $ H $. These schemes are analogous with steepest descent method which is applied on a preconditioned equation obtained by frames instead. We then investigate their convergence via corresponding convergence rates, which are formed by the frame bounds. We also investigate the optimal case, which leads to the exact solution of the equation. The first scheme refers to the case where $H$ is a real separable Hilbert space, but in the second scheme, we drop this assumption.
0

97
109


Hassan
Jamali
Department of Mathematics, Faculty of Mathematics and Computer Sciences, ValieAsr University of Rasanjan, Rafsanjan, Iran.
Iran
jamali@vru.ac.ir


Mohsen
Kolahdouz
Department of Mathematics, Faculty of Mathematics and Computer Sciences, ValieAsr University of Rasanjan, Rafsanjan, Iran.
Iran
mkolahdouz@stu.ac.ir
Hilbert space
Operator equation
Frame
Preconditioning
Steepest descent method
Convergence rate
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1

Some Common Fixed Point Results for Generalized $alpha_*$$psi$contractive Multivalued Mappings on Ordered Metric Spaces with Application to Initial Value Problem
https://scma.maragheh.ac.ir/article_244089.html
10.22130/scma.2020.121445.753
1
In 2012, Samet, et al. introduced the notion of $alpha$$psi$contractive type mappings. They have been establish some fixed point theorems for the mappings on complete metricspaces. In this paper, we introduce the notion of generalized $alpha_*$$psi$contractive multivalued mappings and we give some related fixed point results on ordered metric spaces via application to an initial value problem.
0

111
128


Sajjad
Pahlavany
Department of pure Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.
Iran
golparco@gmail.com


Jalal
Hassanzadeh Asl
Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University Tabriz, Iran.
Iran
jalal.hasanzadeh172@gmail.com


Shahram
Rezapour
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Iran
sh.rezapour@azaruniv.edu
Common fixed points
Generalized $alpha_*$$psi$contractive multivalued mappings
Order closed
Partially ordered set
Weakly increasing
[[1] I. Altun and V. Rakocevic, Ordered cone metric spaces and fixed point results, CAMWAD0900221,(2009).##[2] A. AminiHarandi, Coupled and tripled fixed point theory in partially ordered metric spaces with application to initial value problem, Math. Compute. Modelling, (2012).##[3] B.C. Dhage, Condensing mappings and applications to existence theorems for common solution of differential equations, Bull. Korean Math. Soc., 36 (3),(1999), pp. 565578.##[4] B.C. Dhage, D. ORegan and R.P. Agarwal, Common fixed theorems for a pair of countably condensing mappings in ordered Banach spaces, J. Apple. Math Stoch. Anal., 16 (3),(2003), pp. 243248.##[5] Y. Feng and S. Liu, Fixed point theorems for multivalued increasing operators in partially ordered spaces, Soochow J. Math., 30 (4),(2004), pp. 461469.##[6] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications Nonlinear Analysis. Theory, Methods & Applications., 11 (1987), pp. 623632.##[7] J. Hasanzadeh Asl, Common fixed point theorems for $alpha$$psi$contractive type mappings, Int. J. Anal.,(2013), Article ID 654659, 7 pages.##[8] J. Hasanzadeh Asl, Sh. Rezapour and N. Shahzad, On fixed points of $alphapsi$contractive multifunction's, Fixed Point Theory Appl., 212 (2012), 7 pages.##[9] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for $alpha$$psi$contractive type mappings, Nonlinear Analysis, 75 (2012), pp. 21542165.##[10] Hu Xinqi and Ma Xiaoyan, Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces, Nonlinear Analysis, 74 (2011), pp. 64516458.##]
1

Interior SchauderType Estimates for HigherOrder Elliptic Operators in GrandSobolev Spaces
https://scma.maragheh.ac.ir/article_244074.html
10.22130/scma.2021.521544.893
1
In this paper an elliptic operator of the $m$th order $L$ with continuous coefficients in the $n$dimensional domain $Omega subset R^{n} $ in the nonstandard GrandSobolev space $W_{q)}^{m} left(Omega right), $ generated by the norm $left , cdot , right _{q)} $ of the GrandLebesgue space $L_{q)} left(Omega right), $ is considered. Interior Schaudertype estimates play a very important role in solving the Dirichlet problem for the equation $Lu=f$. The considered nonstandard spaces are not separable, and therefore, to use classical methods for treating solvability problems in these spaces, one needs to modify these methods. To this aim, based on the shift operator, separable subspaces of these spaces are determined, in which finite infinitely differentiable functions are dense. Interior Schaudertype estimates are established with respect to these subspaces. It should be noted that Lebesgue spaces $L_{q} left(Gright), $ are strict parts of these subspaces. This work is a continuation of the authors of the work cite{28}, which established the solvability in the small of higher order elliptic equations in grandSobolev spaces.
0

129
148


Bilal
Bilalov
Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Azerbaijan
b_bilalov@mail.ru


Sabina
Sadigova
Khazar University, Baku, Azerbaijan and Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Azerbaijan
s_sadigova@mail.ru
Elliptic operator
Higherorder
Interior Schaudertype Estimates
GrandSobolev space
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