Abstract
Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham (2006), Lakshmikantham and Ciric (2009) and many others.
Highlights
The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions cf. 1–31
Bhaskar and Lakshmikantham 8, Nieto and Rodrıguez-Lopez 28, Ran and Reurings, and Agarwal et al 1 presented some new results for contractions in partially ordered metric spaces
Bhaskar and Lakshmikantham 8 noted that their theorem can be used to investigate a large class of problems and discussed the existence and uniqueness of solution for a periodic boundary value problem
Summary
The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions cf. 1–31. The aim of this paper is to extend the results of Lakshmikantham and Ciric 24 for a mixed monotone nonlinear contractive mapping in the setting of partially ordered quasi-metric spaces with a Q-function q.
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