Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, a finite family of equilibrium functions {G(i)}(i=1,...,K), a contraction f with coefficient 0 < alpha < 1 and a strongly positive linear bounded operator A with coefficient (gamma) over bar > 0. Let 0 < gamma < (gamma) over bar/alpha. Assuming there are common equilibrium points of the family {G(i)}i=(1,...,K) which are also fixed points for {T(n)}, we define a suitable sequence which strongly converges to the unique such point which also satisfies the variational inequality <(A - gamma f)x*, x - x*> >= 0 for all the x in the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2009 Elsevier Ltd. All rights reserved.

An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings

COLAO, Vittorio;MARINO, Giuseppe
2009

Abstract

Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, a finite family of equilibrium functions {G(i)}(i=1,...,K), a contraction f with coefficient 0 < alpha < 1 and a strongly positive linear bounded operator A with coefficient (gamma) over bar > 0. Let 0 < gamma < (gamma) over bar/alpha. Assuming there are common equilibrium points of the family {G(i)}i=(1,...,K) which are also fixed points for {T(n)}, we define a suitable sequence which strongly converges to the unique such point which also satisfies the variational inequality <(A - gamma f)x*, x - x*> >= 0 for all the x in the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2009 Elsevier Ltd. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/136039
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