On Enriched Weakly Contractive Maps in Hilbert Spaces

Abstract

This paper introduces a class of enriched weakly contractive mappings for approximating a non-Picard average operator on a closed convex subset of Hilbert spaces. By imposing the enriched weakly mapping on the average operator, we establish and prove some results concerning convergence theorems (strong and weak), stability, and convergent rate. The validity and generality of the new class of enriched weakly mappings are examined with the aid of practical examples. The results harmonize and improve some recent results on enriched contractive-type mappings.