Composite extragradient implicit rule for solving a hierarch variational inequality with constraints of variational inclusion and fixed point problems

Journal of inequalities and applications

article

Lu-Chuan Ceng¹  Meijuan Shang² 

[1] Department of Mathematics, Shanghai Normal University;College of Science, Shijiazhuang University

关键词: Gradient-like implicit rule;    System of variational inequalities;    Variational inclusions;    W -mappings;    Uniform convexity;    Uniform smoothness;   

DOI  :  10.1186/s13660-020-2306-1

学科分类：电力

来源: SpringerOpen

【 摘 要 】

Let X be a uniformly convex and q-uniformly smooth Banach space with $1< q\leq 2$. In the framework of this space, we are concerned with a composite gradient-like implicit rule for solving a hierarchical monotone variational inequality with the constraints of a system of monotone variational inequalities, a variational inclusion and a common fixed point problem of a countable family of nonlinear operators $\{S_{n}\}^{\infty }_{n=0}$. Our rule is based on the Korpelevich extragradient method, the perturbation mapping, and the W-mappings constructed by $\{S_{n}\}^{\infty }_{n=0}$.

【 授权许可】

CC BY