$FG$-coupled fixed point theorems for contractive type mappings in partial cone metric spaces

Gurucharan Singh Saluja

Abstract


The concept of $FG$-coupled fixed point is a generalization of coupled fixed point introduced by {\it Guo and Lakshmikantham} [7] in 1987. In this paper, we define $FG$-coupled fixed point in partial cone metric spaces for the mappings $F\colon X\times Y\to X$ and $G\colon Y\times X\to Y$ and prove some $FG$-coupled fixed point theorems for contractive type mappings in the setting of complete partial cone metric spaces. Furthermore, we provide some consequences of the established results. An illustrative example and an application to the system of nonlinear integral equation are given. Our results extend and generalize several results in the existing literature, mainly our results extend and generalize the results of {\it Prajisha and Shaini} [18] and {\it Sabetghadam et al.} [25].

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