, Volume 57, Issue 1, pp 89–108 | Cite as

A new hybrid algorithm for a system of equilibrium problems and variational inclusion

  • Thanyarat Jitpeera
  • Poom Kumam


The purpose of this paper is to consider a shrinking projection method of finding the common element of the set of common fixed points for a finite family of a ξ-strict pseudo-contraction, the set of solutions of a systems of equilibrium problems and the set of solutions of variational inclusions. Then, we prove strong convergence theorems of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend recent results announced by Peng, Wang, Shyu and Yao (J Inequal Appl, 2008:15, Article ID 720371, 2008), Takahashi, Takeuchi and Kubota (J Math Anal Appl 341:276–286, 2008), Takahashi and Takahashi (Nonlinear Anal 69:1025–1033, 2008) and many others.


Generalized mixed equilibrium problem Fixed point Variational inequality Nonexpansive mapping Inverse-strongly monotone mapping 

Mathematics Subject Classification (2000)

47H09 47H05 49J05 49J25 


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Copyright information

© Università degli Studi di Ferrara 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology Thonburi, KMUTTBangkokThailand
  2. 2.Centre of Excellence in Mathematics, CHEBangkokThailand

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