University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Coincidence Point Results for Different Types of $ H_b^{+} $-contractions on $m_b$-Metric Spaces13124407510.22130/scma.2020.131553.836ENSushanta KumarMohantaDepartment of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India.not applicableShilpaPatraDepartment of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India.Journal Article20200724In 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 new<br />classes of $H_b^+ $-contractions for a pair of multi-valued and single-valued mappings and discuss their coincidence points. Some examples are provided to justify the validity of our main results.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Joint Continuity of Bi-multiplicative Functionals334424086110.22130/scma.2020.127223.795ENAbbasZivari-KazempourDepartment of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.MohamadValaeiDepartment of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.Journal Article20200507For Banach algebras $mathcal{A}$ and $mathcal{B}$, we show that if $mathfrak{A}=mathcal{A}times mathcal{B}$ is unital, then each bi-multiplicative mapping from $mathfrak{A}$ into a semisimple commutative Banach algebra $mathcal{D}$ is jointly continuous. This conclusion generalizes a famous result due to<br />$check{text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-multiplicative functionals on $mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$. University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}left( sright) $-Metric Spaces456224230010.22130/scma.2020.127414.799ENEbruAltiparmakDepartment of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.0000-0001-6722-0807IbrahimKarahanDepartment of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.Journal Article20200512In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Some Properties of Complete Boolean Algebras637124230410.22130/scma.2020.127693.802ENAliMolkhasiDepartment of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.0000-0003-1603-2237Journal Article20200527The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all real-valued 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Second Module Cohomology Group of Induced Semigroup Algebras738424230810.22130/scma.2020.130935.826ENMohammad RezaMiriFaculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.EbrahimNasrabadiFaculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.https://orcid.org/0000-0002-0842-492XKianoushKazemiFaculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.Journal Article20200713For 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Two Equal Range Operators on Hilbert $C^*$-modules859624293410.22130/scma.2020.130093.821ENAli RezaJanfadaDepartment of Mathematics, Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Iran.JavadFarokhi-OstadDepartment of Basic sciences, Birjand University of Technology, Birjand 9719866981, Iran.0000-0000-0000-0000Journal Article20200701In this paper, number of properties, involving invertibility, existence of Moore-Penrose 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 Moore-Penrose 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 Moore-Penrose inverse are illustrated.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations9710924407110.22130/scma.2020.123786.771ENHassanJamaliDepartment of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.MohsenKolahdouzDepartment of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.Journal Article20200330In 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 self-adjoint 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Some Common Fixed Point Results for Generalized $alpha_*$-$psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem11112824408910.22130/scma.2020.121445.753ENSajjadPahlavanyDepartment of pure Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.JalalHassanzadeh AslDepartment of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University Tabriz, Iran.0000-0001-8978-6030ShahramRezapourDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Journal Article20200313In 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 metric<br />spaces. In this paper, we introduce the notion of generalized $alpha_*$-$psi$-contractive multi-valued mappings and we give some related fixed point results on ordered metric spaces via application to an initial value problem.University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces12914824407410.22130/scma.2021.521544.893ENBilalBilalovInstitute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.0000-0003-0750-9339Sabina RahibSadigovaKhazar University, Baku, Azerbaijan and Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.0000-0003-4654-0494Journal Article20201221In 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 non-standard Grand-Sobolev space $W_{q)}^{m} left(Omega right), $ generated by the norm $left| , cdot , right| _{q)} $ of the Grand-Lebesgue space $L_{q)} left(Omega right), $ is considered. Interior Schauder-type estimates play a very important role in solving the Dirichlet problem for the equation $Lu=f$. The considered non-standard 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 Schauder-type 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 grand-Sobolev spaces.