Coupled fixed point theorems for nonlinear contractions without mixed monotone property

Fixexd point theory and applications

Wutiphol Sintunavarat²  Yeol Je Cho²  Poom Kumam³ 

[1] Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, Korea;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand

关键词: coupled fixed point;    F-invariant set;    transitive property;    mixed monotone property;    partially ordered set;   

DOI  :  10.1186/1687-1812-2012-170

学科分类：数学（综合）

来源: SpringerOpen

【 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. MSC:47H10, 54H25.

【 授权许可】

CC BY