Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Sat, 01 May 2021 00:00:00 +0430Sat, 01 May 2021 00:00:00 +0430Coincidence Point Results for Different Types of $ H_b^{+} $-contractions on $m_b$-Metric Spaces
https://scma.maragheh.ac.ir/article_244075.html
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.Joint Continuity of Bi-multiplicative Functionals
https://scma.maragheh.ac.ir/article_240861.html
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&nbsp; 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 $n=2$.&nbsp;Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}\left( s\right) $-Metric Spaces
https://scma.maragheh.ac.ir/article_242300.html
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.Some Properties of Complete Boolean Algebras
https://scma.maragheh.ac.ir/article_242304.html
The main result of this paper is a characterization of the strongly algebraically closed algebras in the&nbsp; lattice of all real-valued continuous functions and the equivalence classes of $\lambda$-measurable. We shall provide conditions&nbsp; which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice&nbsp; and $(B,\, \sigma)$ is a Hausdorff space&nbsp; and $B$ satisfies&nbsp; the&nbsp;&nbsp; $G_\sigma$ property, then $B$ carries a strictly positive Maharam submeasure.Second Module Cohomology Group of Induced Semigroup Algebras
https://scma.maragheh.ac.ir/article_242308.html
For a discrete semigroup $ S $ and a left multiplier operator&nbsp; $T$ on&nbsp; $S$, 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,&nbsp; 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&nbsp; $E_{T}$ are subsemigroups of idempotent elements in $S$ and $S_{T}$,&nbsp;&nbsp; respectively.&nbsp; Finally, we show thet, for every odd $n\in\mathbb{N}$,&nbsp; $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1(S_{T}),\ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.Two Equal Range Operators on Hilbert $C^*$-modules
https://scma.maragheh.ac.ir/article_242934.html
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&nbsp; are presented. Natural decompositions of operators with closed range enable us to find some relations of the product of operators with&nbsp; Moore-Penrose inverses under the condition that they have&nbsp; the same ranges&nbsp; 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.Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations
https://scma.maragheh.ac.ir/article_244071.html
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.Some Common Fixed Point Results for Generalized $\alpha_*$-$\psi$-contractive Multi-valued Mappings on Ordered Metric Spaces with Application to Initial Value Problem
https://scma.maragheh.ac.ir/article_244089.html
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&nbsp; application to an initial value problem.Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces
https://scma.maragheh.ac.ir/article_244074.html
In this paper&nbsp; an elliptic operator of the $m$-th order&nbsp; $L$ 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.&nbsp; Interior&nbsp; Schauder-type estimates&nbsp; 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.&nbsp; Interior&nbsp; Schauder-type estimates&nbsp; are established with respect to these subspaces. It should be noted that Lebesgue spaces $L_{q} \left(G\right)\, $ are strict&nbsp;&nbsp; parts of these subspaces. This work is a continuation of the authors&nbsp; of the work \cite{28}, which established the solvability in the small of higher order elliptic equations in grand-Sobolev spaces.Fixed Points of $p$-Hybrid $L$-Fuzzy Contractions
https://scma.maragheh.ac.ir/article_244325.html
In this paper, the notion of $p$-hybrid $L$-fuzzy contractions in the framework of $b$-metric space is introduced. Sufficient conditions for existence of common $L$-fuzzy fixed points under such contractions are also investigated. The established ideas are generalizations of many concepts in fuzzy mathematics. In the case where our postulates are reduced to their classical variants, the concept presented herein merges and extends several significant and well-known fixed point theorems in the setting of both single-valued and multi-valued mappings in the corresponding literature of discrete and computational mathematics.&nbsp; A few of these special cases are pointed out and discussed. In support of our main hypotheses, a nontrivial example is provided.A Generalized Class of Univalent Harmonic Functions Associated with a Multiplier Transformation
https://scma.maragheh.ac.ir/article_244326.html
We define a new subclass of univalent harmonic mappings using multiplier transformation and investigate various properties like necessary and sufficient conditions, extreme points, starlikeness,&nbsp; radius of convexity. We prove that the class is closed under harmonic convolutions and convex combinations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.On Some Linear Operators Preserving Disjoint Support Property
https://scma.maragheh.ac.ir/article_244939.html
The aim of this work is to characterize all bounded linear operators $T:\lpi\rightarrow\lpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $\lpi$ are in the class of such operators, where $2\neq p\in [1,\infty )$ and $I$ is a non-empty set. We extend preserving disjoint support property to linear operators on $\mathfrak{c}_{0}(I).$ At the end, we obtain some equivalent properties of isometries on Banach spaces.Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
https://scma.maragheh.ac.ir/article_244940.html
The present paper seeks to prove the existence and uniqueness of solutions to stochastic evolution equations in Hilbert spaces driven by both Poisson random measure and Wiener process with non-Lipschitz drift term. The proof is provided by the theory of measure of noncompactness and condensing operators. Moreover, we give some examples to illustrate the application of our main theorem.Bicomplex Frames
https://scma.maragheh.ac.ir/article_244941.html
We define in a natural way the bicomplex analog of the frames (bc-frames) in the setting of&nbsp; bicomplex infinite Hilbert spaces, and we characterize them in terms of their idempotent components. We also extend some classical results from frames theory to bc-frames and show that some of them do not remain valid for bc-frames in general. The construction of bc-frame operators and Weyl--Heisenberg bc-frames are also discussed.Integral $K$-Operator Frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$
https://scma.maragheh.ac.ir/article_245093.html
In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from a Hilbert $C^{\ast}$-module $\mathcal{H}$ to&nbsp; itself denoted by $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $.&nbsp; We give some properties relating to some constructions of integral $K$-operator frames and to operators preserving&nbsp; integral $K$-operator frame and we establish some new results.Characteristics of Solutions of Fractional Hybrid Integro-Differential Equations in Banach Algebra
https://scma.maragheh.ac.ir/article_245096.html
In this paper, we discuss the existence results for a class of hybrid initial value problems of Riemann-Liouville fractional differential equations. Our investigation is based on the Dhage hybrid fixed point theorem, remarks and some special cases will be discussed. The continuous dependence of the unique solution on one of its functions will be proved.