Journal of Applied Mathematics and Computing

, Volume 32, Issue 1, pp 19–38 | Cite as

A new iterative algorithm of solution for equilibrium problems, variational inequalities and fixed point problems in a Hilbert space

  • Phayap Katchang
  • Poom Kumam


In this paper, we introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for β-inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in a Hilbert space. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. As applications, at the end of paper we utilize our results to study some convergence problem for finding the zeros of maximal monotone operators. Our results are generalizations and extensions of the results of Yao and Liou (Fixed Point Theory Appl. Article ID 384629, 10 p., 2008), Yao et al. (J. Nonlinear Convex Anal. 9(2):239–248, 2008) and Su and Li (Appl. Math. Comput. 181(1):332–341, 2006) and some recent results.


Nonexpansive mapping Fixed point Equilibrium problem Variational inequality Viscosity approximation method 

Mathematics Subject Classification (2000)

46C05 47D03 47H09 47H10 47H20 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2009

Authors and Affiliations

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

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