A new modified block iterative algorithm for uniformly quasi-phi-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems

作者：Saewan Siwa****; Kumam Poom^*

来源：Fixed Point Theory and Applications, 2011, 35.

DOI：10.1186/1687-1812-2011-35

• modified block iterative algorithm
• inverse-strongly monotone operator
• variational inequality
• a system of generalized mixed equilibrium problem
• uniformly quasi-phi-asymptotically nonexpansive mapping

In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-phi-asymptotically nonexpansive mappings, the set of the variational inequality for an alpha-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works. 2000 MSC: 47H05; 47H09; 47H10.

• 出版日期2011