Coupled fixed point theorems for nonlinear contractions without mixed monotone property

被引：0

作者：

Wutiphol Sintunavarat

Poom Kumam

Yeol Je Cho

机构：

[1] Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok

[2] Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju

来源：

Fixed Point Theory and Applications | / 2012卷 / 1期

基金：

新加坡国家研究基金会;

关键词：

Coupled fixed point; F-invariant set; Mixed monotone property; Partially ordered set; Transitive property;

D O I：

10.1186/1687-1812-2012-170

中图分类号：

学科分类号：

摘要：

In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fixed point of the given mapping. Further, we apply our results to the existence of a coupled fixed point of the given mapping in partially ordered metric spaces. Moreover, some applications to integral equations are presented. © 2012 Sintunavarat et al.; licensee Springer.

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