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

Lu-Chuan Ceng; Yeong-Cheng Liou; Tzu-Chien Yin; Lu-Chuan Ceng; Yeong-Cheng Liou; Tzu-Chien Yin

doi:10.3934/math.20231077

AIMS Mathematics

2023, Volume 8, Issue 9: 21138-21160. doi: 10.3934/math.20231077

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Research article

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

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2.
Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, and Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan
3.
Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 29 April 2023 Revised: 06 June 2023 Accepted: 15 June 2023 Published: 03 July 2023
MSC : 47H09, 47H10, 47J20, 47J25

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.
- pseudomonotone variational inequality,
- Mann-type accelerated projection method,
- line-search method,
- common fixed point,
- Bregman distance,
- Bregman projection
Citation: Lu-Chuan Ceng, Yeong-Cheng Liou, Tzu-Chien Yin. On Mann-type accelerated projection methods for pseudomonotone variational inequalities and common fixed points in Banach spaces[J]. AIMS Mathematics, 2023, 8(9): 21138-21160. doi: 10.3934/math.20231077

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Abstract

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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