Solving integral equations via orthogonal hybrid interpolative RI-type contractions

Fixed Point Theory and Applications Pub Date : 2024-02-01 DOI:10.1186/s13663-023-00759-6

Menaha Dhanraj, Arul Joseph Gnanaprakasam, Santosh Kumar

引用次数: 0

Abstract

In this paper, we initiate the fixed point theorems for an orthogonal hybrid interpolative Riech Istrastescus type contractions map on orthogonal b-metric spaces to modify this class proficiently. Also, we provide some examples supporting our main results. Finally, we provide an application to solve the existence and uniqueness of an integral equation with numeric results, which is powerful in a greater way.

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通过正交混合插值 RI 型收缩求解积分方程

在本文中，我们提出了正交混合插值里奇-伊斯特斯特斯库斯型收缩图在正交 b 计量空间上的定点定理，以熟练地修改这一类。此外，我们还提供了一些例子来支持我们的主要结果。最后，我们提供了一个用数值结果求解积分方程的存在性和唯一性的应用，这在更大程度上是强大的。

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

Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.