矩形b-度量空间的Ekeland变分原理

On Ekeland’s Variational Principle in Rectangular b-mertic Spaces

Ekeland变分原理在不动点理论中占据着重要地位,它在优化理论,控制理论、临界点理论等数学的许多领域都有应用,也是研究偏微分方程的有力工具。从二十世纪七十年代Ekeland提出了著名的Ekeland变分原理至今,国内外许多学者致力于Ekeland变分原理的研究,取得了许多重要的研究成果。本文主要结合矩形b-度量空间的特点和性质,给出矩形b-度量空间的Ekeland变分原理以及Caristi不动点定理。

Ekeland′s variational principle plays an important role in fixed point theory.It has applications in many fields such as optimization theory,control theory,critical point theory and others.It is also a powerful tool for studying partial differential equations.Since Ekeland proposed the famous Ekeland variational principle in the 1970s,many experts at home and abroad have devoted themselves to the study of Ekeland′s variational principle and have obtained many important research results.In this paper,the Ekeland variational principle and Caristi fixed point theorem in rectangular b-metric spaces are given by combining the characteristics and properties of rectangular b-metric spaces.