Hybrid shrinking iterative solutions to convex feasibility problems and a system of generalized mixed equilibrium problems

Volume 9, Issue 6, pp 4798--4813 http://dx.doi.org/10.22436/jnsa.009.06.116

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Authors

Youbing Xiong - Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China.

Abstract

The purpose of this paper is to propose a new hybrid shrinking iterative scheme for approximating common elements of the set of solutions to convex feasibility problems for countable families of weak relatively nonexpansive mappings of a set of solutions to a system of generalized mixed equilibrium problems. A strong convergence theorem is established in the framework of Banach spaces. The results extend those of other authors, in which the involved mappings consist of just finitely many ones.

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Keywords

• Weak relatively nonexpansive mappings
• relatively nonexpansive mappings
• hybrid iteration scheme
• convex feasibility problems
• generalized mixed equilibrium problems.

MSC

•  47H09
•  47H10
•  47J25

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