A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs

Autor:	Wongvisarut Khuangsatung, Akarate Singta, Atid Kangtunyakarn
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	G-variational inequality problem G-inverse strongly monotone mapping G-nonexpansive mapping Regularization method Directed graph Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-25 (2024)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-024-03089-2
Popis:	Abstract This article considers and investigates a variational inequality problem and fixed-point problems in real Hilbert spaces endowed with graphs. A regularization method is proposed for solving a G-variational inequality problem and a common fixed-point problem of a finite family of G-nonexpansive mappings in the framework of Hilbert spaces endowed with graphs, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 187, 2015) and Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018). Under certain conditions, a strong convergence theorem of the proposed method is proved. Finally, we provide numerical examples to support our main theorem. The numerical examples show that the speed of the proposed method is better than some recent existing methods in the literature.
Databáze:	Directory of Open Access Journals
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