Abstract:Let $E$ be a uniformly smooth and uniformly convex real Banach space. We study perturbation-resilient inertial Krasnosel'skii-type hybrid retraction schemes for a countable family of generalized nonexpansive mappings satisfying the NST-condition with a family $\Gamma$. The main result shows that strong convergence is preserved when the exact $\phi$-Fejér decrease condition is replaced by a summably perturbed version. Under suitable structural assumptions on the generated shrinking sets, we prove that the resulting sequence converges strongly to the sunny generalized nonexpansive retraction $R_{F(\Gamma)}v_0$. This provides a stability refinement of existing error-free hybrid retraction methods and gives a framework for treating computational inaccuracies such as approximate projections and inexact operator evaluations. We also discuss a Bregman--Fejér interpretation of the method and formulate a Bregman--projection analogue under the additional structural assumptions required in the general Bregman setting.
From: Markjoe Uba Ph.D. [view email]
[v1]
Sat, 30 May 2026 04:47:53 UTC (13 KB)
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