Coupled coincidence point theorems for nonlinear contractions under (F,g) -invariant set in cone metric spaces

Abstract

We extend the recent results of coupled coincidence point theorems of by weakening the concept of mixed g-monotone property. We also give an example of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by the results of Shatanawi et. al. but can be applied to our results. The main results extend and unify the results of Shatanawi et. al. and many results of the coupled fixed point theorems of Sintunavarat et. al. (2012).

Coincidence point theorem for a new type of contraction on metric spaces

“…We prove a coincidence point result for an F -g-contraction. For more study on Fcontractions one may refer to [3,4,[7][8][9][10] and on coincidence points to [1,2,5,6].…”

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

“…Further, in [3] Batra et al proved some coupled fixed and coincidence results using functions taking values in [0, 1) as a coefficient in different contractive conditions. In this paper we use the concept of an (F,g)-invariant set and extend the results of Batra et al [2,3] as we establish the existence of coupled coincidence point for mappings F : X × X → X and g : X → X satisfying nonlinear contraction under c-distance in cone metric spaces having an (F, g)-invariant subset with functions taking values in [0, 1) as a coefficient in different contractive conditions .…”

“…For more study on coupled fixed point theory see [1,6,10,11,12,15,16,18]. Recently Cho et al [5] introduced a new concept of c-distance in cone metric spaces which is a cone version of w-distance of Kada et al In [2] Batra et al established coupled fixed point theorems for weak contraction mappings by using the concept of (F, g)-invariant set and c-distance in partially ordered cone metric spaces. Further, in [3] Batra et al proved some coupled fixed and coincidence results using functions taking values in [0, 1) as a coefficient in different contractive conditions.…”

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).…”