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Open AccessFeature PaperArticle

Implicit Extragradient-Like Method for Fixed Point Problems and Variational Inclusion Problems in a Banach Space

Department of Liberal Arts, Gyeongnam National University of Science and Technology, Jinju-Si 52725, Gyeongsangnam-do, Korea
Symmetry 2020, 12(6), 998; https://doi.org/10.3390/sym12060998
Received: 7 May 2020 / Revised: 31 May 2020 / Accepted: 3 June 2020 / Published: 11 June 2020
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
In a uniformly convex and q-uniformly smooth Banach space with q ( 1 , 2 ] , one use VIP to indicate a variational inclusion problem involving two accretive mappings and CFPP to denote the common fixed-point problem of an infinite family of strict pseudocontractions of order q. In this paper, we introduce a composite extragradient implicit method for solving a general symmetric system of variational inclusions (GSVI) with certain VI and CFPP. We then investigate its convergence analysis under some weak conditions. Finally, we consider the celebrated LASSO problem in Hilbert spaces. View Full-Text
Keywords: banach space; implicit method; system of variational inclusions; fixed point problem banach space; implicit method; system of variational inclusions; fixed point problem
MDPI and ACS Style

Cho, S.Y. Implicit Extragradient-Like Method for Fixed Point Problems and Variational Inclusion Problems in a Banach Space. Symmetry 2020, 12, 998.

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