University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Coincidence Point Results for Different Types of $ H_b^{+} $-contractions on $m_b$-Metric Spaces
1
31
EN
Sushanta
Kumar
Mohanta
not applicable
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India.
mohantawbsu@rediffmail.com
Shilpa
Patra
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India.
shilpapatrabarasat@gmail.com
10.22130/scma.2020.131553.836
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 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.
$m_b$-metric,$m_b$-Cauchy sequence,$H_b^+ $-contraction,Coincidence point
https://scma.maragheh.ac.ir/article_244075.html
https://scma.maragheh.ac.ir/article_244075_42ed0cbfeb77fafaef4f69651987a520.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Joint Continuity of Bi-multiplicative Functionals
33
44
EN
Abbas
Zivari-Kazempour
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
zivari6526@gmail.com
Mohamad
Valaei
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
mohamad.valaei@abru.ac.ir
10.22130/scma.2020.127223.795
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<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 $n=2$.
Jointly continuous,Bi-multiplicative functional,Almost bi-multiplicative
https://scma.maragheh.ac.ir/article_240861.html
https://scma.maragheh.ac.ir/article_240861_e6375ff83f49e906b56ffeaaf06256ae.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}left( sright) $-Metric Spaces
45
62
EN
Ebru
Altiparmak
0000-0001-6722-0807
Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.
ebru.altiparmak@erzurum.edu.tr
Ibrahim
Karahan
Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.
ibrahimkarahan@erzurum.edu.tr
10.22130/scma.2020.127414.799
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.
Generalized Geraghty contraction,Fixed point,Partial $b_{v}left( sright) $ metric spaces,Generalized metric space
https://scma.maragheh.ac.ir/article_242300.html
https://scma.maragheh.ac.ir/article_242300_0007c9963381ef9edcf6d0b06e90eb30.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Some Properties of Complete Boolean Algebras
63
71
EN
Ali
Molkhasi
0000-0003-1603-2237
Department of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.
molkhasi@gmail.com
10.22130/scma.2020.127693.802
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.
$q^prime$-compactness,Strongly algebraically closed algebras,Complete Boolean algebras
https://scma.maragheh.ac.ir/article_242304.html
https://scma.maragheh.ac.ir/article_242304_dd36edfbe215f4011e11996eac789ce2.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Second Module Cohomology Group of Induced Semigroup Algebras
73
84
EN
Mohammad Reza
Miri
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
mrmiri@birjand.ac.ir
Ebrahim
Nasrabadi
https://orcid.org/0000-0002-0842-492X
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
nasrabadi@birjand.ac.ir
Kianoush
Kazemi
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Birjand, Iran.
kianoush.kazemi@birjand.ac.ir
10.22130/scma.2020.130935.826
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.
second module cohomology group,inverse semigroup,induced semigroup,semigroup algebra
https://scma.maragheh.ac.ir/article_242308.html
https://scma.maragheh.ac.ir/article_242308_8206cd5c01689d1cfa1ad72adb684128.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Two Equal Range Operators on Hilbert $C^*$-modules
85
96
EN
Ali Reza
Janfada
Department of Mathematics, Faculty of Mathematics Science and Statistics, University of Birjand, Birjand 9717851367, Iran.
ajanfada@birjand.ac.ir
Javad
Farokhi-Ostad
0000-0000-0000-0000
Department of Basic sciences, Birjand University of Technology, Birjand 9719866981, Iran.
javadfarrokhi90@gmail.com
10.22130/scma.2020.130093.821
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.
Closed range,Moore-Penrose inverse,Hilbert $C^*$-module
https://scma.maragheh.ac.ir/article_242934.html
https://scma.maragheh.ac.ir/article_242934_c58e189ca1efe772f3a6141d850c6905.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations
97
109
EN
Hassan
Jamali
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.
jamali@vru.ac.ir
Mohsen
Kolahdouz
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.
mkolahdouz@stu.ac.ir
10.22130/scma.2020.123786.771
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 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.
Hilbert space,Operator equation,Frame,Preconditioning,Steepest descent method,Convergence rate
https://scma.maragheh.ac.ir/article_244071.html
https://scma.maragheh.ac.ir/article_244071_85781e3d1440a36d832856bfda468567.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Some Common Fixed Point Results for Generalized $alpha_*$-$psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem
111
128
EN
Sajjad
Pahlavany
Department of pure Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.
golparco@gmail.com
Jalal
Hassanzadeh Asl
0000-0001-8978-6030
Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University Tabriz, Iran.
jalal.hasanzadeh172@gmail.com
Shahram
Rezapour
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
sh.rezapour@azaruniv.edu
10.22130/scma.2020.121445.753
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 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.
Common fixed points,Generalized $alpha_*$-$psi$-contractive multi-valued mappings,Order closed,Partially ordered set,Weakly increasing
https://scma.maragheh.ac.ir/article_244089.html
https://scma.maragheh.ac.ir/article_244089_b489011c507a4bee670fd9528a45e6ee.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
18
2
2021
05
01
Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces
129
148
EN
Bilal
Bilalov
0000-0003-0750-9339
Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
b_bilalov@mail.ru
Sabina
Rahib
Sadigova
0000-0003-4654-0494
Khazar University, Baku, Azerbaijan and Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
s_sadigova@mail.ru
10.22130/scma.2021.521544.893
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(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.
Elliptic operator,Higher-order,Interior Schauder-type Estimates,Grand-Sobolev space
https://scma.maragheh.ac.ir/article_244074.html
https://scma.maragheh.ac.ir/article_244074_10d98a26bec3cb9947f17137508ea500.pdf