Coupled and tripled coincidence point results without compatibility

Nawab Hussain,Abdul Latif,Masood Hussain Shah

doi:10.1186/1687-1812-2012-77

Abstract

Abstract In this article, we introduce a new and simple approach to coupled and tripled coincidence point theory. By using our method, we establish coupled coincidence point results of Lakshmikantham and Ćirić, Binayak et al., Alotaibi and Alsulami without any type of commutativity condition on F and g. We also use our technique to prove tripled coincidence point results of Borcut and Berinde without commutativity of maps. Also, we give a supporting example of non-commuting, non-compatible mappings where the above mentioned results can not be applied. Mathematics Subject Classification: Primary, 47H10; Secondary, 54H25; 34B15.

Highlights

Existence of a fixed point for contraction type mappings in partially ordered metric spaces has been considered recently by Ran and Reurings [1], Agarwal et al [2], Bhaskar and Lakshmikantham [3], Nieto and López [4], and Luong and Thuan [5].Using the concept of commuting maps and mixed g-monotone property, Lakshmikantham and Ćirić [6] established the existence of coupled coincidence point results to generalize the results of Bhaskar and Lakshmikantham [3]
We prove the above mentioned coupled and tripled coincidence results without any type of commutativity condition on F and g
Luong and Thuan [5] presented some coupled fixed point theorems for a mixed monotone mapping in a partially ordered metric space which are generalizations of the results of Bhaskar and Lakshmikantham [3]

Summary

Introduction

Existence of a fixed point for contraction type mappings in partially ordered metric spaces has been considered recently by Ran and Reurings [1], Agarwal et al [2], Bhaskar and Lakshmikantham [3], Nieto and López [4], and Luong and Thuan [5].Using the concept of commuting maps and mixed g-monotone property, Lakshmikantham and Ćirić [6] established the existence of coupled coincidence point results to generalize the results of Bhaskar and Lakshmikantham [3]. Using the concept of commuting maps and mixed g-monotone property, Lakshmikantham and Ćirić [6] established the existence of coupled coincidence point results to generalize the results of Bhaskar and Lakshmikantham [3].

Results

Conclusion