Back
 AM  Vol.2 No.10 , October 2011
Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems
Abstract: In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.
Cite this paper: nullL. Chen and J. Huang, "Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1213-1220. doi: 10.4236/am.2011.210169.
References

[1]   W.-Y. Zeng, N.-J Huang and C.-W. Zhao, “Viscosity Approximation Methods for Generalized Mixed Equili-brium Problems and Fixed Points of a Sequence of Non-expansive Mappings,” Fixed Point Theory Applications, Vol. 2008, 2008, Article ID 714939.

[2]   D. R. Sahu, N.-C. Wong and J.-C. Yao, “On Convergence Analysis of an Iterative Algorithm for Finding Common Solution of Generalized Mixed Equilibrium Problems and Fixed Point Problems,” Mathematical Inequlities and Applications, Article in Press.

[3]   W. Takahashi and K. Shimoji, “Convergence Theorems for Nonexpansive Mappings and Feasibility Problems,” Mathematical and Computer Modelling, Vol. 32, No. 11, 2000, pp. 1463-1471. doi:10.1016/S0895-7177(00)00218-1

[4]   L.-C. Ceng and J.-C. Yao, “A Hybrid Iterative Scheme for Mixed Equilibrium Problems and Fixed Point Problems,” Journal of Computational and Applied Mathematics, Vol. 214, No. 1, 2008, pp. 186-201. doi:10.1016/j.cam.2007.02.022

[5]   H. K. Xu, “Viscosity Approximation for Nonexpansive Mappings,” Journal of Mathematical Analysis and Applications, Vol. 298, No. 1, 2004, pp. 279-291. doi:10.1016/j.jmaa.2004.04.059

[6]   T. Suzuki, “Strong Convergence of Krasnoselskii and Mann’s Type Se-quences for One-Parameter Nonexpansive Semigroups without Bochner Integrals,” Journal of Mathematical Analysis and Applications, Vol. 305, No. 1, 2005, pp. 227-239. doi:10.1016/j.jmaa.2004.11.017

[7]   S. B. Nadle Jr., “Multi-Valued Contraction Mappings,” Pacific Journal of Mathematics, Vol. 30, 1969, pp. 475-488.

 
 
Top