A new class of computationally efficient algorithms for solving fixed-point problems and variational inequalities in real Hilbert spaces

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

Other (Strategic Research Themes)

Publication Details

Author list: Wiyada Kumam; Habib ur Rehman; Poom Kumam;

Publisher: SpringerOpen

Publication year: 2023

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2023

Issue number: 1

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85152533089&doi=10.1186%2fs13660-023-02948-8&partnerID=40&md5=44e6a70ee799b258d9e12306b08639b3

Languages: English-Great Britain (EN-GB)

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Abstract

A family of inertial extragradient-type algorithms is proposed for solving convex pseudomonotone variational inequality with fixed-point problems, where the involved mapping for the fixed point is a ρ-demicontractive mapping. Under standard hypotheses, the generated iterative sequence achieves strong convergence to the common solution of the variational inequality and fixed-point problem. Some special cases and sufficient conditions that guarantee the validity of the hypotheses of the convergence statements are also discussed. Numerical applications in detail illustrate the theoretical results and comparison with existing methods. © 2023, The Author(s).

Keywords

Inertial iterative schemes, ρ-demicontractive mapping