Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 641479, 19 pages
http://dx.doi.org/10.1155/2012/641479
Research Article

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

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Mathematics, Tianjin No. 8 Middle School, Tianjin 300252, China

Received 11 November 2011; Accepted 17 December 2011

Academic Editor: Rudong Chen

Copyright © 2012 Haiqing Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. E. Browder, โ€œFixed-point theorems for noncompact mappings in Hilbert space,โ€ Proceedings of the National Academy of Sciences of the United States of America, vol. 53, pp. 1272โ€“1276, 1965. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  2. S. Reich, โ€œStrong convergence theorems for resolvents of accretive operators in Banach spaces,โ€ Journal of Mathematical Analysis and Applications, vol. 75, no. 1, pp. 287โ€“292, 1980. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  3. F. E. Browder, โ€œConvergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces,โ€ Archive for Rational Mechanics and Analysis, vol. 24, pp. 82โ€“90, 1967. View at Google Scholar
  4. Y. Song and S. Xu, โ€œStrong convergence theorems for nonexpansive semigroup in Banach spaces,โ€ Journal of Mathematical Analysis and Applications, vol. 338, no. 1, pp. 152โ€“161, 2008. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  5. A. Moudafi, โ€œViscosity approximation methods for fixed-points problems,โ€ Journal of Mathematical Analysis and Applications, vol. 241, no. 1, pp. 46โ€“55, 2000. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  6. H.-K. Xu, โ€œViscosity approximation methods for nonexpansive mappings,โ€ Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 279โ€“291, 2004. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  7. S. Plubtieng and R. Punpaeng, โ€œFixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces,โ€ Mathematical and Computer Modelling, vol. 48, no. 1-2, pp. 279โ€“286, 2008. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH
  8. R. Chen and Y. Song, โ€œConvergence to common fixed point of nonexpansive semigroups,โ€ Journal of Computational and Applied Mathematics, vol. 200, no. 2, pp. 566โ€“575, 2007. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  9. W. Takahashi, Nonlinear Functional Analysis—Fixed Point Theory and Its Applications, Yokohama Publishers, Yokohama, Japan, 2000.
  10. K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, vol. 83 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1984.
  11. H.-K. Xu, โ€œStrong convergence of an iterative method for nonexpansive and accretive operators,โ€ Journal of Mathematical Analysis and Applications, vol. 314, no. 2, pp. 631โ€“643, 2006. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  12. F. E. Browder, โ€œSemicontractive and semiaccretive nonlinear mappings in Banach spaces,โ€ Bulletin of the American Mathematical Society, vol. 74, pp. 660โ€“665, 1968. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  13. F. E. Browder, โ€œConvergence theorems for sequences of nonlinear operators in Banach spaces,โ€ Mathematische Zeitschrift, vol. 100, pp. 201โ€“225, 1967. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet
  14. W. Takahashi and Y. Ueda, โ€œOn Reich's strong convergence theorems for resolvents of accretive operators,โ€ Journal of Mathematical Analysis and Applications, vol. 104, no. 2, pp. 546โ€“553, 1984. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH ยท View at MathSciNet