处理涉及模糊（\mathcal{H}\）-收缩映射的定点结果的简捷方法

Fixed Point Theory and Applications Pub Date : 2020-10-01 DOI:10.1186/s13663-020-00682-0

Hayel N. Saleh, Mohammad Imdad, Md Hasanuzzaman

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引用次数: 0

摘要

在本文中，我们采用了一种简短而锐化的方法来证明《Wardowski，模糊集合系统》125:245-252，2013）和其他相关文章中使用的涉及模糊 $\mathcal{H}$ 合约映射的定点结果。在此过程中，我们能够放宽早期作者使用的一些条件，这反过来又对早期作者提出的一些开放性问题给出了肯定的答案。

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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A short and sharpened way to approach fixed point results involving fuzzy $\mathcal{H}$-contractive mappings

In the present paper, we adopt a short and sharpened approach to prove fixed point results involving fuzzy $\mathcal{H}$ -contractive mappings utilized in (Wardowski, Fuzzy Sets Syst. 125:245–252, 2013) and other related articles. In this process, we are able to relax some conditions utilized by earlier authors which in turn yields affirmative answers to some open questions raised by earlier authors.

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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.