On parallel Mann-type extragradient algorithms for systems of variational inequalities with constraints of variational inclusion and fixed point problems
Applicable Nonlinear Analysis, Volume 1, Issue 2, December 2024, Pages: 206–225
LU-CHUAN CENG
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
OUAYL CHADLI
Department of Mathematics and System Engineering, Florida Institute of Technology, Melbourne, Florida, USA
CHING-FENG WEN
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Taiwan
Abstract
In a uniformly convex and \(\mathfrak q\)-uniformly smooth Banach space with \(\mathfrak q \in (1,2]\), let the VI indicate a variational inclusion for two accretive operators and let the CFPP denote a common fixed point problem of a countable family of nonexpansive mappings. In this paper, we introduce a parallel Manntype extragradient algorithm for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints. We then prove the strong convergence of the suggested algorithm to a solution of the GSVI with the VI and CFPP constraints under some suitable assumptions. As applications, we apply our main result to the variational inequality problem (VIP), split feasibility problem (SFP) and LASSO problem in Hilbert spaces.
Cite this Article as
Lu-Chuan Ceng, Ouayl Chadli, and Ching-Feng Wen, On parallel Mann-type extragradient algorithms for systems of variational inequalities with constraints of variational inclusion and fixed point problems, Applicable Nonlinear Analysis, 1(2), 206–225, 2024