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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 789043, 12 pages
http://dx.doi.org/10.1155/2012/789043
Research Article

Fixed Point and Weak Convergence Theorems for ( 𝛼 , 𝛽 ) -Hybrid Mappings in Banach Spaces

1Center for General Education, Fooyin University, 151 Jinxue Road, Daliao District, Kaohsiung 83102, Taiwan
2Department of Finance, Nan Jeon Institute of Technology, 178 Chaoqin Road, Yenshui District, Tainan 73746, Taiwan
3Center for General Education, Southern Taiwan University, 1 Nantai Street, Yongkang District, Tainan 71005, Taiwan
4Department of Industrial Management, National Pingtung University of Science and Technology, 1 Shuefu Road, Neopu, Pingtung 91201, Taiwan

Received 28 September 2011; Accepted 29 November 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Tian-Yuan Kuo 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. S. Iemoto and W. Takahashi, “Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 12, pp. e2082–e2089, 2009. View at Publisher · View at Google Scholar
  2. F. Kohsaka and W. Takahashi, “Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces,” Archiv der Mathematik, vol. 91, no. 2, pp. 166–177, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. Takahashi, “Fixed point theorems for new nonlinear mappings in a Hilbert space,” Journal of Nonlinear and Convex Analysis, vol. 11, no. 1, pp. 79–88, 2010. View at Zentralblatt MATH
  4. P. Kocourek, W. Takahashi, and J.-C. Yao, “Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces,” Taiwanese Journal of Mathematics, vol. 14, no. 6, pp. 2497–2511, 2010. View at Zentralblatt MATH
  5. D. Butnariu and A. N. Iusem, Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization, vol. 40, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. I. Ciorãnescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, vol. 62, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990. View at Zentralblatt MATH
  7. Y. Y. Huang, J. C. Jeng, T. Y. Kuo, and C. C. Hong, “Fixed point and weak convergence theorems for point-dependent λ-hybrid mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2011, article 105, 2011. View at Publisher · View at Google Scholar
  8. Z. Opial, “Weak convergence of the sequence of successive approximations for nonexpansive mappings,” Bulletin of the American Mathematical Society, vol. 73, pp. 591–597, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. A. Noor, “New approximation schemes for general variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217–229, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Aslam Noor, “Some developments in general variational inequalities,” Applied Mathematics and Computation, vol. 152, no. 1, pp. 199–277, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. A. Noor, “General variational inequalities and nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 331, no. 2, pp. 810–822, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet