Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914620267036672 |
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| author | Uba, Markjoe O. |
| author_facet | Uba, Markjoe O. |
| contents | 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 $Γ$. The main result shows that strong convergence is preserved when the exact $ϕ$-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 $R_{F(Γ)}v_0$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings Uba, Markjoe O. Functional Analysis 47H09, 47H10, 47J25 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 $Γ$. The main result shows that strong convergence is preserved when the exact $ϕ$-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 $R_{F(Γ)}v_0$. 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. |
| title | Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings |
| topic | Functional Analysis 47H09, 47H10, 47J25 |
| url | https://arxiv.org/abs/2606.00528 |