Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings

作者：Ceng, L. C.; Al-Mazrooei, A. E.; Abdou, A. A. N.; Latif, A.^*

来源：Abstract and Applied Analysis, 2013, 2013: 102820.

DOI：10.1155/2013/102820

• STRONG-CONVERGENCE THEOREMS
• FIXED-POINT PROBLEMS
• VISCOSITY APPROXIMATION METHODS
• WEAK-CONVERGENCE
• EXTRAGRADIENT METHOD
• SPLIT FEASIBILITY
• BANACH
• ALGORITHMS
• SEQUENCES
• FAMILY

We introduce hybrid and relaxed Mann iteration methods for a general system of variational inequalities with solutions being also common solutions of a countable family of variational inequalities and common fixed points of a countable family of nonexpansive mappings in real smooth and uniformly convex Banach spaces. Here, the hybrid and relaxed Mann iteration methods are based on Korpelevich's extragradient method, viscosity approximation method, and Mann iteration method. Under suitable assumptions, we derive some strong convergence theorems for hybrid and relaxed Mann iteration algorithms not only in the setting of uniformly convex and 2-uniformly smooth Banach space but also in a uniformly convex Banach space having a uniformly Gateaux differentiable norm. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

• 出版日期2013
• 单位上海大学; 上海师范大学