Parallel composite-type extragradient implicit method for a system of variational inclusions with the common fixed-point constraint of pseudocontractive mappings
Fixed Point Methods and Optimization, Volume 1, Issue 2, December 2024, Pages 125–144
LU-CHUAN CENG
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
ESKANDAR NARAGHIRAD
Department of Mathematics, Faculty of Sciences, Yasouj University, Yasouj 75918, Iran
CHING-FENG WEN
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Taiwan
JEN-CHIH YAO
Center for General Education, China Medical University, Taichung, Taiwan
Abstract
In a uniformly convex and \(q\)-uniformly smooth Banach space with \(q\in(1,2]\), 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 \(\ell\)-uniformly Lipschitzian pseudocontractive mappings. In this paper, we introduce a parallel composite-type extragradient implicit method for solving a general system of variational inclusions (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 appropriate 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, Eskandar Naraghirad, Ching-Feng Wen, And Jen-Chih Yao, Parallel composite-type extragradient implicit method for a system of variational inclusions with the common fixed-point constraint of pseudocontractive mappings,Fixed Point Methods and Optimization, 1(2), 125–144, 2024