Existence Theorems of Fixed Points for \((\mathcal{Z}, \lambda)\)-Enriched Contraction in Convex Metric Spaces

Abstract

In this paper, we introduce the simulation function \(\zeta:[0, \infty)\times[0, \infty)\rightarrow \mathbb{R}\) and define a mapping \(T:X\rightarrow X\) as a \((\mathcal{Z}, \lambda)\)-enriched contraction with respect to \(\zeta\in\mathcal{Z}\) and \(\lambda\in[0, 1)\), which generalizes the Banach contraction principle. To indicate the relevance of our new results, we present some important particular cases of the fixed point theorem along with supportive examples.