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2009•Journal of Shangqiu Vocational and Technical CollegeRequires access

Strong Convergence Theorem for a Generalized Equilibrium Problem and Fixed Points of a Finite Family of Nonexpansive Mappings in A Hilbert Space

Rudong Chen

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Abstract

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of a generalized equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space.This main theorem extends a recent result of Satoru Takahashi and WararuTakahashi[Satoru Takahashi,Wataru Takahashi,Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69(2008)1025-1033].

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In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of a generalized equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space.This main theorem extends a recent result of Satoru Takahashi and WararuTakahashi[Satoru Takahashi,Wataru Takahashi,Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69(2008)1025-1033].

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Available abstract

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of a generalized equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space.This main theorem extends a recent result of Satoru Takahashi and WararuTakahashi[Satoru Takahashi,Wataru Takahashi,Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69(2008)1025-1033].

Key concepts: Hilbert space, Mathematics, Convergence (economics), Fixed point, Nonlinear system, Space (punctuation), Set (abstract data type), Applied mathematics

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Strong Convergence Theorem for a Generalized Equilibrium Problem and Fixed Points of a Finite Family of Nonexpansive Mappings in A Hilbert Space — Research Paper | ScholarLens