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2012 Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
Dan Zhang, Xiaolong Qin, Feng Gu
J. Appl. Math. 2012(SI03): 1-13 (2012). DOI: 10.1155/2012/417234

Abstract

Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S = { T ( s ) : 0 s < } with a common fixed point, a contraction f with the coefficient 0 < α < 1 , and a strongly positive linear bounded self-adjoint operator A with the coefficient γ ¯ > 0. Let 0 < γ < γ ¯ / α . It is proved that the sequence { x n } generated by the iterative method x 0 H ,  x n + 1 = α n γ f ( x n ) + β n x n + ( ( 1 - β n ) I - α n A ) ( 1 / s n ) 0 s n T ( s ) x n d s ,  n 0 converges strongly to a common fixed point x * F ( S ) , where F ( S ) denotes the common fixed point of the nonexpansive semigroup. The point x * solves the variational inequality ( γ f - A ) x * , x - x * 0 for all x F ( S ) .

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Dan Zhang. Xiaolong Qin. Feng Gu. "Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces." J. Appl. Math. 2012 (SI03) 1 - 13, 2012. https://doi.org/10.1155/2012/417234

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1250.47079
MathSciNet: MR2880849
Digital Object Identifier: 10.1155/2012/417234

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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