Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings

Abstract

Let $\E$ be a uniformly smooth and uniformly convex real Banach space. We study an inertial hybrid retraction method for a countable sequence of mappings satisfying the NST-condition and an approximate $ϕ$-Fejér inequality with vanishing errors. We prove that the generated sequence converges strongly to the sunny generalized nonexpansive retraction of the initial point onto the common fixed-point set. The theorem admits vanishing error sequences that need not be summable and therefore contains the summable-error setting as a special case. We also establish a Bregman-projection analogue and provide illustrative examples.