On Mann-type accelerated projection methods for pseudomonotone variational inequalities and common fixed points in Banach spaces-Reference-Cited by-同舟云学术

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

Published:2023 Issue:9 Volume:8 Page:21138-21160
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ceng Lu-Chuan¹,Liou Yeong-Cheng²,Yin Tzu-Chien³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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