Abstract

In this paper, we define enriched $(\psi,\varphi_\lambda)$-weakly contractive map in convex metric spaces where $\psi$ is continuous on $[0,+\infty)$ and $\varphi_\lambda$ is not continuous on $[0,+\infty)$ and prove the existence and uniqueness of fixed points of these maps in complete convex metric spaces. We provide an example in support of our result.

Keywords and Phrases

Contraction, enriched contraction, $(\lambda, c)$-enriched contraction, enriched $(\psi,\varphi_\lambda)$-weakly contractive map.

A.M.S. subject classification

47H10, 54H25.

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