Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces

被引：4

作者：

Cobzas, S. ^{[1
]}

机构：

[1] Babes Bolyai Univ, Fac Math & Comp Sci, Cluj Napoca 400084, Romania

来源：

QUAESTIONES MATHEMATICAE | 2023年 / 46卷 / 04期

关键词：

reordered quasi-metric space; completeness in quasi-metric spaces; variational principles; Ekeland variational principle; Takahashi minimization principle; fixed point; Caristi fixed point theorem; PARTIALLY ORDERED SETS; FIXED-POINT THEOREMS; VARIATIONAL-PRINCIPLES; COMPLETENESS; EXISTENCE;

D O I：

10.2989/16073606.2022.2042417

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove versions of Ekeland, Takahashi and Caristi principles in pre-ordered quasi-metric spaces, the equivalence between these principles, as well as their equivalence to some completeness results for the underlying quasi-metric space. These extend the results proved in S. Cobzas, Topology Appl. 265 (2019), 106831, 22, for quasi-metric spaces. The key tools are Picard sequences for some special set-valued mappings on a pre-ordered quasi-metric space X, defined in terms of the preorder and of a function phi on X.

引用

页码：791 / 812

页数：22

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