Abstract
The purpose of this paper is to establish a coupled coincidence point theorem for a pair of mappings without MMP (mixed monotone property) in metric spaces endowed with partial order, which is not an immediate consequence of a well-known theorem in the literature. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend some of the results of Bhaskar and Lakshmikantham (Nonlinear Anal. 65:1379-1393, 2006), Choudhury, Metiya and Kundu (Ann. Univ. Ferrara 57:1-16, 2011), Harjani, Lopez and Sadarangani (Nonlinear Anal. 74:1749-1760, 2011) and of Luong and Thuan (Bull. Math. Anal. Appl. 2:16-24, 2010) for the mappings having no MMP. We introduce an example that there exists a common coupled fixed point of the mappings g and F such that F does not satisfy the g-mixed monotone property, and also g and F do not commute.
Highlights
Introduction and preliminariesFixed point theory is one of the famous and traditional theories in mathematics and has a large number of applications
There are a lot of generalizations of the Banach contraction principle in the literature
While Nieto and Rodŕiguez-López [ ] extended the result of Ran and Reurings and applied their main theorems to obtain a unique solution for a first-order ordinary differential equation with periodic boundary conditions
Summary
Introduction and preliminariesFixed point theory is one of the famous and traditional theories in mathematics and has a large number of applications.
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