Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 641479, 19 pages.

Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces

Haiqing Wang, Yongfu Su, and Hong Zhang

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Abstract

Let X be a uniformly convex Banach space and S = { T ( s ) : 0 s < } be a nonexpansive semigroup such that F ( S ) = s > 0 F ( T ( s ) ) . Consider the iterative method that generates the sequence { x n } by the algorithm x n + 1 = α n f ( x n ) + β n x n + ( 1 - α n - β n ) ( 1 / s n ) 0 s n T ( s ) x n d s , n 0 , where { α n } , { β n } , and { s n } are three sequences satisfying certain conditions, f : C C is a contraction mapping. Strong convergence of the algorithm { x n } is proved assuming X either has a weakly continuous duality map or has a uniformly Gâteaux differentiable norm.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 641479, 19 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180273

Digital Object Identifier
doi:10.1155/2012/641479

Mathematical Reviews number (MathSciNet)
MR2889103

Zentralblatt MATH identifier
1235.49028

Citation

Wang, Haiqing; Su, Yongfu; Zhang, Hong. Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 641479, 19 pages. doi:10.1155/2012/641479. https://projecteuclid.org/euclid.jam/1357180273


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