Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 417234, 13 pages.

Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces

Dan Zhang, Xiaolong Qin, and Feng Gu

Full-text: Open access

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 ) .

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 417234, 13 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180293

Digital Object Identifier
doi:10.1155/2012/417234

Mathematical Reviews number (MathSciNet)
MR2880849

Zentralblatt MATH identifier
1250.47079

Citation

Zhang, Dan; Qin, Xiaolong; Gu, Feng. Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 417234, 13 pages. doi:10.1155/2012/417234. https://projecteuclid.org/euclid.jam/1357180293


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