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arXiv · 2606.00528

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

Markjoe O. Uba
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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 $\phi$-Fej\'er 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.

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Markjoe O. Uba. 2026-05-30. Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings. https://arxiv.org/abs/2606.00528

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