Open Access Research

Maximal and minimal point theorems and Caristi's fixed point theorem

Zhilong Li* and Shujun Jiang

Author Affiliations

Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China

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Fixed Point Theory and Applications 2011, 2011:103  doi:10.1186/1687-1812-2011-103

Published: 21 December 2011

Abstract

This study is concerned with the existence of fixed points of Caristi-type mappings motivated by a problem stated by Kirk. First, several existence theorems of maximal and minimal points are established. By using them, some generalized Caristi's fixed point theorems are proved, which improve Caristi's fixed point theorem and the results in the studies of Jachymski, Feng and Liu, Khamsi, and Li.

MSC 2010: 06A06; 47H10.

Keywords:
maximal and minimal point; Caristi's fixed point theorem; Caristi-type mapping; partial order