Strong convergence of shrinking projection methods for quasi-φ-nonexpansive mappings and equilibrium problems

Authors:
Xiaolong Qin;Sun Young Cho;Shin Min Kang
Affiliations:
Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China;Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea;Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea and The RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The purpose of this paper is to consider the convergence of a shrinking projection method for a finite family of quasi-@f-nonexpansive mappings and an equilibrium problem. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property.