Coupled coincidence and common fixed point theorems for hybrid pair of mappings

Fixexd point theory and applications

irić^{1  2}  Mujahid Abbas²  Ljubomir Ć³ 

[1] Department of Mathematics, Faculty of Agriculture, Belgrade, Serbia;Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan;Faculty of Mechanical Engineering, Belgrade, Serbia

关键词: coupled common fixed point;    coupled coincidence point;    coupled point of coincidence;    w-compatible mappings;    F-weakly commuting mappings;   

DOI  :  10.1186/1687-1812-2012-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two single valued maps. In this article, we extend these concepts to multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Two examples are presented to support our results. 2000 Mathematics Subject Classification: 47H10; 47H04; 47H07.

【 授权许可】

CC BY