Journal of Applied Mathematics and Computing

, Volume 29, Issue 1–2, pp 263–280 | Cite as

A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping

Article

Abstract

In this paper, we introduce an iterative scheme by a new hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a real Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under some parametric controlling conditions by the new hybrid method which is introduced by Takahashi et al. (J. Math. Anal. Appl., doi:  10.1016/j.jmaa.2007.09.062, 2007). The results are connected with Tada and Takahashi’s result [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mappings and an equilibrium problem, J. Optim. Theory Appl. 133, 359–370, 2007]. Moreover, our result is applicable to a wide class of mappings.

Keywords

Nonexpansive mapping Monotone mapping Equilibrium problem Variational inequality 

Mathematics Subject Classification (2000)

46C05 47D03 47H09 47H10 47H20 

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Copyright information

© Korean Society for Computational and Applied Mathematics 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology ThonburiBangkokThailand

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