Hybrid Viscosity Approaches to General Systems of Variational Inequalities with Hierarchical Fixed Point Problem Constraints in Banach Spaces

作者：Ceng, Lu-Chuan; Al-Mezel, Saleh A.^*; Latif, Abdul

来源：Abstract and Applied Analysis, 2014, 2014: 945985.

DOI：10.1155/2014/945985

• STRONG-CONVERGENCE THEOREMS
• STEEPEST-DESCENT METHODS
• NONEXPANSIVE-MAPPINGS
• EXTRAGRADIENT METHOD
• SPLIT FEASIBILITY
• COUNTABLE FAMILY
• APPROXIMATION
• SMOOTH

The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich's extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings in X, respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors.

• 出版日期2014
• 单位上海师范大学; 上海大学