Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems

This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of $\alpha$ -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that $\alpha$ -Krasnosel’skiĭ mapping associated with $b$ -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning $b$ -enriched quasinonexpansive mappings have been proved.