Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, 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 We define a suitable Mann type algorithm which strongly converges to the unique solution of the minimization problem(x is an element of C) 1/2 (Ax,x) - h (x), where h is a potential function for f and C is the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2010 Elsevier Ltd. All rights reserved.
Strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings
COLAO, Vittorio;Marino G.
2010-01-01
Abstract
Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, 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 We define a suitable Mann type algorithm which strongly converges to the unique solution of the minimization problem(x is an element of C) 1/2 (Ax,x) - h (x), where h is a potential function for f and C is the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2010 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
