A NEW HYBRID ALGORITHM FOR A COUNTABLE FAMILY OF QUASI-NONEXPANSIVE MAPPINGS AND EQUILIBRIUM PROBLEMS

作者：Cholamjiak Watchara****; Suantai Suthep^*

来源：Journal of Nonlinear and Convex Analysis, 2011, 12(2): 381-398.

• Generalized equilibrium problem
• variational inequality
• strong convergence
• quasi-nonexpansive mapping
• inverse-strongly monotone

In this paper, we introduce and study a new hybrid algorithm for finding common elements of the set of common fixed points of a countable family of quasi-nonexpansive mappings, the set; of solutions of variational inequality and the set of solutions of generalized equilibrium problem. We prove a strong convergence theorem of the purposed algorithm under some control conditions and the NST-condition. We also show that the sequences of W-mappings and K-mappings of families of quasi-nonexpansive mappings satisfy the NST-condition.

• 出版日期2011