Coincidence Point Results for Different Types of $ H_b^{+} $-contractions on $m_b$-Metric Spaces
Sushanta
Mohanta
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India.
author
Shilpa
Patra
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India.
author
text
article
2021
eng
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 multi-valued and single-valued mappings and discuss their coincidence points. Some examples are provided to justify the validity of our main results.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
1
31
https://scma.maragheh.ac.ir/article_244075_42ed0cbfeb77fafaef4f69651987a520.pdf
dx.doi.org/10.22130/scma.2020.131553.836
Joint Continuity of Bi-multiplicative Functionals
Abbas
Zivari-Kazempour
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
author
Mohamad
Valaei
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
author
text
article
2021
eng
For 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$\check{\text{S}}$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 $n=2$.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
33
44
https://scma.maragheh.ac.ir/article_240861_e6375ff83f49e906b56ffeaaf06256ae.pdf
dx.doi.org/10.22130/scma.2020.127223.795
Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}\left( s\right) $-Metric Spaces
Ebru
Altiparmak
Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.
author
Ibrahim
Karahan
Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.
author
text
article
2021
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
45
62
https://scma.maragheh.ac.ir/article_242300_0007c9963381ef9edcf6d0b06e90eb30.pdf
dx.doi.org/10.22130/scma.2020.127414.799
Some Properties of Complete Boolean Algebras
Ali
Molkhasi
Department of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.
author
text
article
2021
eng
The 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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
63
71
https://scma.maragheh.ac.ir/article_242304_dd36edfbe215f4011e11996eac789ce2.pdf
dx.doi.org/10.22130/scma.2020.127693.802
Second Module Cohomology Group of Induced Semigroup Algebras
Mohammad Reza
Miri
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
author
Ebrahim
Nasrabadi
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
author
Kianoush
Kazemi
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
author
text
article
2021
eng
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 $n\in\mathbb{N}$, $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1(S_{T}),\ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
73
84
https://scma.maragheh.ac.ir/article_242308_8206cd5c01689d1cfa1ad72adb684128.pdf
dx.doi.org/10.22130/scma.2020.130935.826
Two Equal Range Operators on Hilbert $C^*$-modules
Ali Reza
Janfada
Department of Mathematics, Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Iran.
author
Javad
Farokhi-Ostad
Department of Basic sciences, Birjand University of Technology, Birjand 9719866981, Iran.
author
text
article
2021
eng
In 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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
85
96
https://scma.maragheh.ac.ir/article_242934_c58e189ca1efe772f3a6141d850c6905.pdf
dx.doi.org/10.22130/scma.2020.130093.821
Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations
Hassan
Jamali
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.
author
Mohsen
Kolahdouz
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.
author
text
article
2021
eng
In this paper, by using the concept of frames, two iterative methods are constructed to solve the operator equation $ Lu=f $ where $ L:H\rightarrow 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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
97
109
https://scma.maragheh.ac.ir/article_244071_85781e3d1440a36d832856bfda468567.pdf
dx.doi.org/10.22130/scma.2020.123786.771
Some Common Fixed Point Results for Generalized $\alpha_*$-$\psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem
Sajjad
Pahlavany
Department of pure Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.
author
Jalal
Hassanzadeh Asl
Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University Tabriz, Iran.
author
Shahram
Rezapour
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
author
text
article
2021
eng
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 multi-valued mappings and we give some related fixed point results on ordered metric spaces via application to an initial value problem.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
111
128
https://scma.maragheh.ac.ir/article_244089_b489011c507a4bee670fd9528a45e6ee.pdf
dx.doi.org/10.22130/scma.2020.121445.753
Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces
Bilal
Bilalov
Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
author
Sabina
Sadigova
Khazar University, Baku, Azerbaijan and Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
author
text
article
2021
eng
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 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(G\right)\, $ 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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
18
v.
2
no.
2021
129
148
https://scma.maragheh.ac.ir/article_244074_10d98a26bec3cb9947f17137508ea500.pdf
dx.doi.org/10.22130/scma.2021.521544.893