Strong convergence of an enriched multi-step iterative scheme for common fixed points of enriched nearly asymptotically pseudocontractive mappings

Abstract

We propose and analyze an enriched multi-step iterative scheme for approximating common fixed points of finite families of enriched nearly uniformly \(L\)-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces. Under mild assumptions on the parameter sequences, we prove strong convergence theorems that extend classical results of Agarwal et al. and Yao and Chen to the enriched multi-operator setting. The proof techniques rely on normalized duality mappings, demiclosedness principles, and convergence lemmas. Crucially, our unified framework accommodates mappings that need not be continuous, thereby addressing a significant gap in the existing literature and broadening the applicability of fixed point theory to more general nonlinear problems.