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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