Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Wed, 01 Mar 2023 00:00:00 +0330Wed, 01 Mar 2023 00:00:00 +0330New Iteration Algorithms for Solving Equilibrium Problems and Fixed Point Problems of Two Finite Families of Asymptotically Demicontractive Multivalued Mappings
https://scma.maragheh.ac.ir/article_701674.html
ln this paper, we introduce a new class of mapping called asymptotically demicontractive multivalued mapping in the setting of a real Hilbert space. Furthermore, a new iteration scheme was constructed, and it was proved that our algorithm converges strongly to the common element of solutions of an equilibrium problem and the set of common fixed points of two finite families of type-one asymptotically demicontractive multivalued mappings without any sum conditions imposed on the finite family of the control sequences. Also, we provided a numerical example to demonstratethe implementablity of our proposed iteration technique. &nbsp;Our results improve, extend and generalize many recently announced results in the currentOn Fixed Points of a General Class of Hybrid Contractions with Ulam-Type Stability
https://scma.maragheh.ac.ir/article_700987.html
In this paper, a new general class of contraction, namely admissible hybrid $(G$-$\alpha$-$\phi)$-contraction is introduced and some fixed point theorems that cannot be deduced from their corresponding ones in metric spaces are proved. The distinction of this family of contractions is that its contractive inequality can be specialized in several ways, depending on multiple parameters. Consequently, several corollaries, including some recently announced results in the literature are highlighted and analyzed. Nontrivial comparative examples are constructed to validate the assumptions of our obtained theorems. We further examine Ulam-type stability and well-posedness for the new contraction proposed herein. In addition, one of our obtained corollaries is applied to set up novel existence conditions for the solution of a class of integral equations. There is an open problem concerning the discretized population balance model, whose solution may be analyzed using the methods established here.Second Hankel Determinant for Certain Subclasses of Bi-starlike Functions Defined by Differential Operators
https://scma.maragheh.ac.ir/article_701228.html
In this paper, we obtain &nbsp;upper bounds of the initial Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert ,$ $\left\vert a_{3}\right\vert $ and $\left\vert a_{4}\right\vert $ and of the Fekete-Szeg&ouml; functional $\left\vert a_{3}-\eta a_{2}^{2}\right\vert $ for certain subclasses of analytic and bi-starlike functions $\mathcal{S}_{\sigma }^{\ast }(\beta,\theta ,n,m)$ in the open unit disk. We have also obtained an upper bound of the functional $\left\vert a_{2}a_{4}-a_{3}^{2}\right\vert $ for the functions in the class $\mathcal{S}_{\sigma }^{\ast }(\beta ,\theta ,n,m)$. Moreover, several interesting applications of the results presented here are also discussed.Hermite-Hadamard, Trapezoid and Midpoint Type Inequalities Involving Generalized Fractional Integrals for Convex Functions
https://scma.maragheh.ac.ir/article_701393.html
We first construct new Hermite-Hadamard type inequalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard fractional integrals. Afterwards, Trapezoid and Midpoint type results involving generalized fractional integrals for functions whose the derivatives in modulus and their certain powers are convex are established. We also recapture the previous results in the particular situations of the inequalities which are given in the earlier works.Fixed Point Results for Multivalued Mapping in $\mathrm{R}$-Metric Space
https://scma.maragheh.ac.ir/article_700985.html
This paper explores certain fixed point results for multivalued mapping in a metric space endowed with an arbitrary binary relation $\mathrm{R}$, briefly written as $\mathrm{R}$-metric space. The fixed point results proved &nbsp;are subjected to contraction conditions corresponding to the multivalued counterpart of $F$-contraction and $F$-weak contraction in $\mathrm{R}$-metric space. The main results unify, extend and generalize the results on multivalued and single-valued mapping in the literature. To support the conclusion, several examples have been provided.Maps Completely Preserving the Quadratic Operators
https://scma.maragheh.ac.ir/article_701631.html
Let $\mathcal{A}$ and $\mathcal{B}$ be standard operator algebras on Banach spaces $\mathcal{X}$ and $\mathcal{Y}$, respectively. Let $\phi: \mathcal{A} \rightarrow \mathcal{B}$ be a bijective map. In this paper, we show that $\phi$ is completely preserving quadratic operator in both directions if and only if $\phi$ is 2-quadratic preserving operator in both directions and if and only if $\phi$ is either an isomorphism or (in the complex case) a conjugate isomorphism.Investigation of the Properties of a New Class of Interpolation Polynomials Based on Fibonacci Numbers
https://scma.maragheh.ac.ir/article_700986.html
In this paper, a class of new polynomials based on Fibonacci sequence using Newton interpolation is introduced. This target is performed once using Newton forward- divided- difference formula and another more using Newton backward- divided- difference formula. Some interesting results are obtained for forward and backward differences. The relationship between forward (and backward) differences and the Khayyam- Pascal's triangle are also examined.A New Iterative Method for Solving Constrained Minimization, Variational Inequality and Split Feasibility Problems in the Framework of Banach Spaces
https://scma.maragheh.ac.ir/article_702159.html
In this paper, we introduce a new type of modified generalized $\alpha$-nonexpansive mapping and establish some fixed point properties and demiclosedness principle for this class of mappings in the framework of &nbsp;uniformly convex Banach spaces. We further &nbsp;propose a new iterative method for approximating a common fixed point of two modified generalized $\alpha$-nonexpansive mappings and present some weak and strong convergence theorems for these mappings in uniformly convex Banach spaces. In addition, we apply our result to solve a &nbsp;convex-constrained minimization problem, variational inequality and split feasibility problem and present some numerical experiments in infinite dimensional spaces to establish the applicability and efficiency of our proposed algorithm. The obtained results in this paper improve and extend &nbsp; some related results in the literature.Duality of Continuous K-g-Frames
https://scma.maragheh.ac.ir/article_702402.html
K-g-frames, as an extension of g-frames and K-frames are one of the active fields in frame theory. In this paper, we &nbsp;consider continuous K-g-frames which are a generalization of discrete K-g-frames. We give the necessary and sufficient conditions to characterize their duals. For example, the canonical dual &nbsp;of a given K-g-frame is described by both its frame operator and its alternate duals.Some Basic Results on Fuzzy Strong $\phi$-b-Normed Linear Spaces
https://scma.maragheh.ac.ir/article_701675.html
Following the definition of fuzzy normed linear space which was introduced by Bag and Samanta in general t-norm settings, in this paper, &nbsp;definition of fuzzy strong $\phi$-b-normed linear space is given. Here the scalar function $|c| $ is replaced by a general function $ \phi(c) $ where $ \phi $ satisfies some properties. Some basic results on finite dimensional &nbsp;fuzzy strong $\phi$-b-normed linear space are studied.On bi-conservative hypersurfaces in the Lorentz-Minkowski 4-space $E_1^4$
https://scma.maragheh.ac.ir/article_703150.html
In the 1920s, D. Hilbert has showed that the tensor of stress-energy, related to a given functional $\Lambda$, is a conservative symmetric bicovariant tensor $\Theta$ at the critical points of $\Lambda$, which means that div$\Theta =0$. As a routine extension, the bi-conservative condition (i.e. div$\Theta_2=0$) on &nbsp;the tensor of stress-bienergy&nbsp; $\Theta_2$ is introduced by G. Y. Jiang (in 1987). This subject has been followed by many mathematicians. In this paper, we study an extended version of bi-conservativity condition on the Lorentz hypersurfaces of the Einstein space. A Lorentz hypersurface $M_1^3$ isometrically immersed into the Einstein space is called $\mathcal{C}$-bi-conservative if it satisfies the condition $n_2(\nabla H_2)=\frac{9}{2} H_2\nabla H_2$, where $n_2$ is the second Newton transformation, $H_2$ is the 2nd mean curvature function on $M_1^3$ and $\nabla$ is the gradient tensor. We show that the $C$-bi-conservative Lorentz hypersurfaces of Einstein space have constant second mean curvature.Dynamical Systems Implemented by Isomorphic Groups of Unitaries
https://scma.maragheh.ac.ir/article_703194.html
Let $\varphi:A\to B$ be an isomorphism of $C^*$-algebras and $I$ be an ideal of $A.$ &nbsp;Introducing the concepts of unitary equivalent and the implemented Finsler modules, we show that the $\frac{A}{I}$-module $\frac{E}{E_{I}}$ and the implemented &nbsp;$\frac{B}{\varphi(I)}$-module &nbsp;$\frac{F}{F_{\varphi(I)}}$ &nbsp;are unitary equivalent. We also, &nbsp;establish a one to one correspondence between &nbsp;the groups $U(E)$ and $U(F)$ of &nbsp;unitaries on full Finsler modules $E$ and $F,$ respectively. &nbsp; Finally, we explain regularized &nbsp;dynamical systems and &nbsp; apply the aforementioned one to one correspondenec to prove that &nbsp;each regularized &nbsp;dynamical system in $U(E)$ implements a &nbsp; regularized &nbsp;dynamical system &nbsp;in $U(F).$