Some fixed-point theorems for mixed monotone operators in partially ordered probabilistic metric spaces

Jun Wu

doi:10.1186/1687-1812-2014-49

Abstract

In this paper, some fixed-point theorems for nonlinear contractive operators in partially ordered Menger probabilistic metric spaces are proved. A new extension theorem of the probabilistic versions of Boyd and Wong’s nonlinear contraction theorem is presented. As a consequence, our main results improve and generalize some recent coupled fixed-point theorems and coincidence-point theorems in (Ciric, Nonlinear Anal. 72:2009-2018, 2010; Jachymski, Nonlinear Anal., 73:2199-2203, 2010; Ciric, Agarwal and Samet, Fixed Point Theory Appl. 2011:56, 2011).

Highlights

Introduction and preliminariesIt is well known that the probabilistic version of the classical Banach contraction principle was proved in by Sehgal and Bharucha-Reid [ ]
In, a truthful probabilistic version of the Banach fixed-point principle for general nonlinear contractions was presented by Ljubomir Ćirić [ ]
The fixed-point theorems in probabilistic metric spaces for other contraction mappings were investigated by many authors, see [ – ] the references therein

Summary

Introduction

Introduction and preliminariesIt is well known that the probabilistic version of the classical Banach contraction principle was proved in by Sehgal and Bharucha-Reid [ ]. The fixed-point theorems in probabilistic metric spaces for other contraction mappings were investigated by many authors, see [ – ] the references therein. We try to extend this probabilistic version theorem to the partially ordered Menger probabilistic metric spaces and establish some fixed-point theorems for monotone operators.

Results

Conclusion