Branciari 型广义计量空间中的广义弱收缩的定点定理

Fixed Point Theory and Applications Pub Date : 2021-01-25 DOI:10.1186/s13663-021-00688-2

Zhiqun Xue, Guiwen Lv

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引用次数: 0

摘要

在本文中，我们得到了一个新的收敛定理，即在较弱条件下，布兰切里类型广义度量空间中弱收缩的定点。该定理的证明过程是全新的，与其他作者的证明过程不同。该定理的一个说明性例子是，新条件是如何扩展已知结果的。

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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A fixed point theorem for generalized \((\psi ,\varphi )\)-weak contractions in Branciari type generalized metric spaces

In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.

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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.