On a new generalization of a Perov-type F-contraction with application to a semilinear operator system

Fixed Point Theory and Applications Pub Date : 2024-03-18 DOI:10.1186/s13663-024-00762-5

Muhammad Sarwar, Syed Khayyam Shah, Kamaleldin Abodayeh, Arshad Khan, Ishak Altun

引用次数: 0

Abstract

This manuscript aims to present new results about the generalized F-contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single and pairs of generalized F-contractions of Hardy–Rogers-type mappings. The established results represent a significant development of numerous previously published findings and results in the existing body of literature. Furthermore, to ensure the practicality and effectiveness of our findings across other fields, we provide an application that demonstrates a unique solution for the semilinear operator system within the Banach space.

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论 Perov 型 F-contraction 的新广义化及其在半线性算子系统中的应用

本手稿旨在提出关于完整向量值度量空间中哈迪-罗杰斯型映射的广义 F-收缩的新结果，并证明哈迪-罗杰斯型映射的单个和成对广义 F-收缩的定点定理。这些既定结果是对之前发表在现有文献中的众多发现和结果的重大发展。此外，为了确保我们的发现在其他领域的实用性和有效性，我们提供了一个应用，展示了巴拿赫空间内半线性算子系统的独特解决方案。

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.