A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces

In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of -fixed points of continuous -pseudocontractive mappings in reflexive real Banach spac...

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Bibliographic Details
Published in:Topological algebra and its applications Vol. 11; no. 1; pp. 545 - 574
Main Authors: Zegeye, Habtu, Boikanyo, Oganeditse A.
Format: Journal Article
Language:English
Published: De Gruyter 01.01.2023
Subjects:
47H05
47H10
47J05
47J20
47J25
47J26
f-fixed point
f-pseudocontractive mapping
fixed point
monotone mapping
pseudocontractive mapping
semi-pseudocontractive mapping
strong convergence
variational inequality
zero points
ISSN:2299-3231, 2299-3231
Online Access:Get full text
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Summary:In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of -fixed points of continuous -pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common -fixed point of continuous -pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.
ISSN:2299-3231
2299-3231
DOI:10.1515/taa-2022-0133