On Mann-type accelerated projection methods for pseudomonotone variational inequalities and common fixed points in Banach spaces

Autor: Lu-Chuan Ceng, Yeong-Cheng Liou, Tzu-Chien Yin
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: AIMS Mathematics, Vol 8, Iss 9, Pp 21138-21160 (2023)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.20231077?viewType=HTML
Popis: In this paper, we investigate two Mann-type accelerated projection procedures with line search method for solving the pseudomonotone variational inequality (VIP) and the common fixed-point problem (CFPP) of finitely many Bregman relatively nonexpansive mappings and a Bregman relatively asymptotically nonexpansive mapping in $ p $-uniformly convex and uniformly smooth Banach spaces. Under mild conditions, we show weak and strong convergence of the proposed algorithms to a common solution of the VIP and CFPP, respectively.
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