Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

IF 3.1 3区数学 Q1 MATHEMATICS

Advances in Difference Equations Pub Date : 2022-08-17 DOI:10.1186/s13662-022-03724-6

Hasanen A. Hammad, Mohamed Elmursi, Rashwan A. Rashwan, Hüseyin Işık

引用次数: 2

Abstract

The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direction. Moreover, two examples are derived to support and document our theoretical results. Finally, to strengthen our paper and its contribution to applications, some convergence results for a class of matrix difference equations are investigated.

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应用不动点方法求解一类新算子的矩阵差分方程

本文的目的是在通常度量空间的设置下，给出一类新的满足Prešić-type有理η-收缩条件的算子。这些算子还得到了新的不动点结果。我们的研究结果概括、扩展并统一了这方面的许多论文。此外，还推导了两个例子来支持和证明我们的理论结果。最后，研究了一类矩阵差分方程的收敛性结果，以加强本文的研究和应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

8.60

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.