Coupled coincidence point results for a generalized compatible pair with applications

Abstract

In this paper, employing a new concept of generalized compatibility of a pair of mappings defined on a product space, certain coupled coincidence point results of mappings involved herein are obtained. We also deduce certain coupled fixed point results without mixed monotone property of F. Our results generalize some recent comparable results in the literature. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results. MSC: 46S40; 47H10; 54H25

Resolving systems of nonlinear integral equations via C-class functions

“…In this paper, we use the notion of C-class of function which is generalization of altering distance function and by using this definition we have improved the results of Hussain, Abbas, Azam and Ahmad (Hussain et al, 2014) in the setting of bmetric space. Also we provide and an application to an integral equation to support our results presented here.…”

“…In this paper we gives Corollary 1.12 that shows the broadening of Corollary 22 in Hussain et al (2014) on b-metric spaces by using the C-class functions. It should be noted that in our example, in Corollary 1.12 which follows the condition (2) there is a great difference from the condition in Corollary 22 in Hussain et al (2014).  is increasing…”

“…(Ansari et al, 2014) . Therefore, in this paper we gives Theorem 1.11 which represents the continuation of Theorem 15 from Hussain et al (2014) on b-metric spaces whit the implementation of the functions of the C-class. However, in our case, in the following Theorem 1.11 the condition (1) highly differs from the condition in Theorem 15 (Hussain et al, 2014 …”

“…There exist continuous functions Hussain et al (2014), Theorem 26) we studied the integral equation (3) and proved that the mapping H has a coupled fixed point that is a solution in…”

Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

“…In [9], Hussain et al introduced the following: F G X X X × → be two mappings. We say that the pair {F,G} is commuting if …”