Parallel Subgradient-like Extragradient Approaches for Variational Inequality and Fixed-Point Problems with Bregman Relatively Asymptotical Nonexpansivity

In a uniformly smooth and p-uniformly convex Banach space, let the pair of variational inequality and fixed-point problems (VIFPPs) consist of two variational inequality problems (VIPs) involving two uniformly continuous and pseudomonotone mappings and two fixed-point problems implicating two unifor...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 15; no. 9; p. 1749
Main Authors: Ceng, Lu-Chuan, Cui, Yun-Ling, Cao, Sheng-Long, Li, Bing, Wang, Cong-Shan, Hu, Hui-Ying
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.09.2023
Subjects:
Algorithms
Asymptotic properties
Banach spaces
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:In a uniformly smooth and p-uniformly convex Banach space, let the pair of variational inequality and fixed-point problems (VIFPPs) consist of two variational inequality problems (VIPs) involving two uniformly continuous and pseudomonotone mappings and two fixed-point problems implicating two uniformly continuous and Bregman relatively asymptotically nonexpansive mappings. This article designs two parallel subgradient-like extragradient algorithms with an inertial effect for solving this pair of VIFPPs, where each algorithm consists of two parts which are of a mutually symmetric structure. With the help of suitable registrations, it is proven that the sequences generated by the suggested algorithms converge weakly and strongly to a solution of this pair of VIFPPs, respectively. Lastly, an illustrative instance is presented to verify the implementability and applicability of the suggested approaches.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym15091749