错位准计量空间中格拉基准收缩型映射的定点结果

Fixed Point Theory and Applications Pub Date : 2020-11-02 DOI:10.1186/s13663-020-00683-z

Joy C. Umudu, Johnson O. Olaleru, Adesanmi A. Mogbademu

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引用次数: 0

摘要

本文证明了一种新引入的格拉基准收缩型映射在更一般的度量空间（称为T-轨道完全错位准度量空间）中的定点结果。Geraghty 准收缩类型映射概括了 Ciric 准收缩映射和文献中的其他 Geraghty 准收缩类型映射。在不对映射施加连续性条件的情况下获得了定点结果，从而进一步推广了文献中的一些其他相关工作。本文举例说明了所获结果的有效性。

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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Fixed point results for Geraghty quasi-contraction type mappings in dislocated quasi-metric spaces

In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric’s quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained without imposing a continuity condition on the mapping, thereby further generalizing some other related work in the literature. An example is given to show the validity of results obtained.

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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.