On Enriched Suzuki Nonexpansive Mappings in P-Uniformly Convex Metric Spaces

This paper introduces and defines the concept of enriched Suzuki nonexpansive mappings T in p-uniformly convex metric spaces, thereby extending earlier results established in Hadamard spaces. We show that the τ-averaged mapping Tτ preserves the fixed points of T. In addition, we prove that Tτ is quasi-nonexpansive and that the sequence generated by the Mann iteration converges to a fixed point of both T and its averaged counterpart Tτ. We further establish both ∆-convergence and strong convergence of the Mann iteration sequence for the τ-averaged mapping. Additionally, we present an illustrative example of an enriched Suzuki nonexpansive mapping within p-uniformly convex metric spaces.