Journal of Mathematical Analysis and Convex Optimization
Volume:4 Issue: 1, 2023

We introduce an iterative algorithm for split equality fixed point and null point problem for Lipschitzian quasi-pseudocontractivemappings and maximal monotone operators which includes split equality feasibility problem, split equality fixed problem, split equality null pointproblem and other problem related to fixed point problems. Moreover, we establish a strong convergence results in real Hilbert spaces undersome suitable conditions and reduce our main result to above-mentioned problems. Finally, we apply the study to split equality feasibility problem (SEFP), split equality equilibrium problem (SEEP), split equality variational inequality problem (SEVIP) and split equality optimization problem (SEOP). The results presented in the paper extend and improve many recent results.

A bounded linear operator T on a locally convex space X is balanced convex-cyclic if there exists a vector x 2 X such that the balanced convex hull of orb(T; x) is dense in X.A balanced convex-polynomial is a balanced convex combination of monomials f1; z; z2; z3; : : : g.In this paper we prove that the balanced convex-polynomials are dense in Lp() when ([-1; 1]) = 0.Our results are used to characterize which multiplication operators on various real Banach spaces are balanced convex-cyclic.Also,it is shown for certain multiplicationoperators that every nonempty closed invariant balanced convex-set is a closed invariant subspace.

In this paper, we use some bi-sequences of positive numbers to define weighted dynamical metrics. Then we show that, replacing the Bowen dynamical metric by the weighted metric, the definition of pressure for asymptotically sub-additive potentials, including measure-theoretic and topological, is not affected. This generalizes some known results for pressure, defined using mean metrics and continuous potentials.

In this paper, we deal with the existence of a non-trivialsolution for the following fractional  discrete boundary-value problem for any $k in [1,T]_{mathbb{N}_{0}}$begin{equation*}begin{cases}_{T+1}nabla_k^{alpha}left( ^{}_knabla_{0}^{alpha}(u(k))right)+{^{}_knabla}_{0}^{alpha}left( ^{}_{T+1}nabla_k^{alpha}(u(k))right)+phi_{p}(u(k))=lambda f(k,u(k)), u(0)= u(T+1)=0,end{cases}end{equation*}where $0< alpha<1$ and $^{}_knabla_{0}^{alpha}$ is  the left nabla discrete fractional difference  and $^{}_{T+1}nabla_k^{alpha}$ is the right nabla discrete fractional difference   $f: [1,T]_{mathbb{N}_{0}}timesmathbb{R}tomathbb{R}$ isa continuous function, $lambda>0$ is a parameter and  $phi _{p}$ is the so called $p$-Laplacianoperator defined as $phi _{p}(s)=|s|^{p-2}s$ and $1

The class of Bryant-type metrics is a  natural extension of the class of 4-th root Finsler metrics which are used in Biology as ecological metrics. In this paper, we  classify  Bryant-type metrics admitting an $(alpha, beta)$-metric on a two-dimensional  manifold and show that it contains two classes of non-Riemannian $(alpha, beta)$-metrics, specially Randers-type metrics. This might provide fine insights into a possible theory of deformations of Finsler norms.

In this article, we have solved the Fokker-Planck Equation(FPE) by numericalmethod. For the approximate solution of this problem, we used of polynomial basis functionsand the least squares method. The least squares method together with the satisfier function isused to transform the the FPE to the solution of equation systems. Also we debate the con-vergence of the presented technique. Then we consider illustrative examples to represent theapplicability and validity of the this method.

The paper is devoted to continuous frames and continuous Riesz basis in Hilbert C*-modules. We define a continuous Riesz basis in Hilbert C*-modules and investigate the relationship between a continuous Riesz basis and an L^2-independent Bessel mapping. Also, we show that a continuous frame is a continuous Riesz basis if and only if it is a Riesz-type frame. Finally, we give the relation between two continuous Riesz bases in Hilbert C*-modules.

Let $mathcal{A}$ and $mathcal{B}$ be two standard operator algebra on  Banach spaces $mathcal{X}$ and $mathcal{Y}$, respectively. In this paper, we determine the forms of the surjective maps from $mathcal{A}$ onto $mathcal{B}$ such that completely preserve zero triple Jordan product in both directions.

This paper tries to show that there is only one solution for problem of fractional $q$-differential equations with  Hilfer type, and it does so by using a particular method known as Schaefer's fixed point theorem  and the Banach contraction principle. After that, we create a integral  type of the  problem for nonlocal condition. Next, we show that Ulam stability is true. The Gr"{o}wnwall rule for singular kernels of the equations helps to show our findings are correct. We confirm our findings by giving a few practical examples.

In this paper we introduce a new sequence of mappings in connection to Hermite-Hadamard type inequality. Some bounds and refinements of Hermite-Hadamard inequality for convex functions via this  sequence  are given

ln this paper, we introduce an iterative scheme for approximating a common element of the fixed point sets of a finite family of a multivalued -hemicontractive mappings, the set of solutions of a finite family of variational inequality problems and the set of solutions of a finite family of equilibrium problems. Using our scheme, we establish strong convergence theorems of the aforementioned problems in the framework of real Hilbert spaces. Our results improve, extend, generalise and unify many recent results in this direction.

Data Envelopment Analysis (DEA) is a Nonparametric method for measuring of the performance of decision-making units (DMUs) - which do not need to have or compute a firm's production function, which is often difficult to calculate. In this article, we evaluate the units under review in terms of cost efficiency, and the units in terms of spending and production over several periods, and the rate of improvement or regression of each of these units. Considering the minimal use of resources and consuming less money, the improvement or retreat of the recipient's decision unit in terms of cost was examined by presenting a method based on solving linear programming models using the productivity index is Malmquist Global. Finally, by designing and solving a numerical example, we emphasize and test the applicability of the material presented in this article.