Weak convergence theorems for inertial Krasnoselskii-Mann iterations in the class of enriched nonexpansive operators in Hilbert spaces

Liviu-Ignat Socaciu

doi:10.2478/auom-2025-0013

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Weak convergence theorems for inertial Krasnoselskii-Mann iterations in the class of enriched nonexpansive operators in Hilbert spaces

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 33 (2025): Issue 1 (March 2025)

By: Liviu-Ignat Socaciu

Open Access

|Apr 2025

Abstract

In this paper, we present some results about the aproximation of fixed points of nonexpansive and enriched nonexpansive operators. In order to approximate the fixed points of enriched nonexpansive mappings, we use the Krasnoselskii-Mann iteration for which we prove weak convergence theorem and the theorem which offers the convergence rate analysis.

Our results in this paper extend some classical convergence theorems from the literature from the case of nonexpansive mappings to that of enriched nonexpansive mappings. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2025-0013 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 261 - 280

Submitted on: Nov 18, 2023

Accepted on: Feb 7, 2024

Published on: Apr 2, 2025

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

weak convergence,

inertial iteration,

nonexpansive operator,

enriched non-expansive operator,

Hilbert space

Related subjects:

Mathematics,

General mathematics

© 2025 Liviu-Ignat Socaciu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 1 (March 2025)