Stability Results for Enriched Contraction Mappings in Convex Metric Spaces

Abstract

In this paper, we obtain some stability results of fixed point sets for a sequence of enriched contraction mappings in the setting of convex metric spaces. In particular, two types of convergence of mappings, namely, $\left(\mathcal{G}\right)$ -convergence and $\left(H\right)$ -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation.