论文标题
ekeland差异原理及其等效物在$ t_1 $ -quasi均匀的空间
Ekeland variational principle and its equivalents in $T_1$-quasi-uniform spaces
论文作者
论文摘要
本文涉及ekeland差异原理（EKVP）及其等效物（Caristi-Kirk固定点定理，高桥最小化原理，ekvp的oettli-théra平衡版本）在准均匀的空间中。这些扩展了非线性肛门Hamel证明的一些结果。 \ textbf {62}（2005），913--924，在统一空间中，以及各种作者在准中空间中证明的空间。 $ f $ -quasi-gauge空间的情况，这是Fang，J。Math引入的$ f $ gouge空间的非对称版本。肛门。应用。 \ textbf {202}（1996），398--412也被考虑。本文以Arutyunov和Zh的Gel'man证明的一些最小化原则的准均匀版本结尾。维奇斯。垫。垫。 fiz。 \ textbf {49}（2009），1167--1174和Arutyunov，Proc。 Steklov Inst。数学。 \ textbf {291}（2015），第〜1、24--37号，在完整的度量空间中。 关键词：Ekeland差异原理，高桥最小化原理，平衡问题，均匀的空间，准统一空间，量规空间，准岩石空间，准均匀空间的完整性
The present paper is concerned with Ekeland Variational Principle (EkVP) and its equivalents (Caristi-Kirk fixed point theorem, Takahashi minimization principle, Oettli-Théra equilibrium version of EkVP) in quasi-uniform spaces. These extend some results proved by Hamel, Nonlinear Anal. \textbf{62} (2005), 913--924, in uniform spaces, as well as those proved in quasi-metric spaces by various authors. The case of $F$-quasi-gauge spaces, a non-symmetric version of $F$-gauge spaces introduced by Fang, J. Math. Anal. Appl. \textbf{202} (1996), 398--412, is also considered. The paper ends with the quasi-uniform versions of some minimization principles proved by Arutyunov and Gel'man, Zh. Vychisl. Mat. Mat. Fiz. \textbf{49} (2009), 1167--1174, and Arutyunov, Proc. Steklov Inst. Math. \textbf{291} (2015), no.~1, 24--37, in complete metric spaces. Key words: Ekeland Variational Principle, Takahashi minimization principle, equilibrium problems, uniform spaces, quasi-uniform spaces, gauge spaces, quasi-gauge spaces, completeness in quasi-uniform spaces
