Coupled Coincidence Points of Almost Generalized $(\psi, \phi)$-Weakly Contractive Maps under an $(F, g)$-Invariant Set

Gutti Venkata Ravindranadh Babu, Kidane Koyas Tola

Abstract

Let $(X, d)$ be a metric space and $F : X \times X \rightarrow X$ and $g : X \rightarrow X$ be maps. In this paper, we define almost generalized $(\psi, \phi)$-weakly contractive maps and prove the existence of coupled coincidence points of such maps under an $(F, g)$-invariant set without using the mixed $g$-monotone property  in a metric space setting. We also, apply our results to obtain the existence of coupled coincidence points in  partially ordered metric spaces. Our results generalize the results of Choudhury,  Metiya and Kundu [B.S. Choudhury, N. Metiya, A. Kundu, Coupled coincidence point theorems  in ordered metric spaces, Ann. Univ. Ferrara 57 (2011) 1--16]. We also provide  examples in support of our results.