Coupled coincidence point theorems for mappings without mixed monotone property under c-distance in cone metric spaces

Abstract

Fixed point theory in the field of partially ordered metric spaces has been an area of attraction since the appearance of Ran and Reurings theorem and Nieto and Rodríguez-López theorem. One of the most significant hypotheses of these theorems was the mixed monotone property which has been avoided and replaced by the notion of invariant set in recent years and many statements have been proved using the concept of invariant set. In this paper we show that the invariant condition guides us to prove many similar results to which we were exposed to using the mixed monotone property. We present some examples in support of applicability of our results.

A note on the paper "A fixed point theorems in Sb-metric spaces"

“…the pair (X, S b ) is called an S b -metric space. [2], [4], [5], [9], [11], [13]- [21], [23]- [25], [30], [31], [34]).…”

Coupled fixed point theorems in G b -metric space satisfying some rational contractive conditions

“…( 2012 ), Kadelburg and Radenovic ( 2012 ), Batra and Vashistha ( 2013 ), Batra et al. ( 2014 ), Karapinar and Turkoglu ( 2010 ), Shantanawi ( 2010 ), Aghajani et al. ( 2012 ), Mehta and Joshi ( 2010 ), Malhotra and Bansal ( 2015 ), Karapinar, Bhaskar and Lakshmikantham ( 2006 ), Singh and Singh ( 2014 ) and reference therein.…”

Common Coupled Fixed Point Theorems of Two Mappings Satisfying Generalized Contractive Condition in Cone Metric Space

“…Thus, cone naturally induces a partial order in Banach spaces. In recent years many authors established various coupled fixed point theorems in cone metric space (see [6][7][8][9][10][11][12][13][14][15][16][17] and references there in).…”