Modified inertial viscosity extrapolation method for solving quasi-monotone variational inequality and fixed point problems in real Hilbert spaces

Autor:	Jacob A. Abuchu, Austine E. Ofem, Hüseyin Işık, Godwin C. Ugwunnadi, Ojen K. Narain
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Quasi-monotone operator Variational inequality Strong convergence Inertial extrapolation method Viscosity approximation Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-21 (2024)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-024-03113-5
Popis:	Abstract In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed point constraint of quasi-nonexpansive mappings under the scope of real Hilbert spaces when the underlying cost operator is quasi-monotone. The method involves inertial viscosity approximation and a constructed self-adjustable step size condition that depends solely on the information of the previous step. We establish a strong convergence result of the proposed method under certain mild conditions on the algorithm parameters. Finally, to demonstrate the gain of our method, some numerical examples are presented in comparison with some related methods in literature.
Databáze:	Directory of Open Access Journals
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