Some results on a tripled fixed point for nonlinear contractions in partially ordered G -metric spaces

Fixexd point theory and applications

Abdullah Alotaibi¹  Syed Abdul Mohiuddine¹ 

[1] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: tripled fixed point;    partially ordered set;    mixed monotone mapping;    generalized metric space;   

DOI  :  10.1186/1687-1812-2012-179

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Berinde and Borcut (Nonlinear Anal. 74(15):4889-4897, 2011) have quite recently defined the notion of a triple fixed point and proved some interesting results related to this concept in a partially ordered metric space. In this work we prove some triple fixed point theorem for a mixed monotone mapping satisfying nonlinear contractions in the framework of a generalized metric space endowed with partial order while the idea of a generalized metric space introduced by Mustafa and Sims (J. Nonlinear Convex Anal. 7:289-297, 2006). Further we prove the uniqueness of a coupled fixed point for such a mapping in this setting.

【 授权许可】

CC BY