Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS OF QUASI-NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITY PROBLEMS

  • Li, Meng (Department of Mathematics, Ordnance Engineering College) ;
  • Sun, Qiumei (Department of Mathematics, Ordnance Engineering College) ;
  • Zhou, Haiyun (Department of Mathematics, Ordnance Engineering College)
  • Received : 2012.07.10
  • Accepted : 2013.01.13
  • Published : 2013.09.30
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Abstract

In this paper, a new iterative algorithm involving quasi-nonexpansive mapping in Hilbert space is proposed and proved to be strongly convergent to a point which is simultaneously a fixed point of a quasi-nonexpansive mapping, a solution of an equilibrium problem and the set of solutions of a variational inequality problem. The results of the paper extend previous results, see, for instance, Takahashi and Takahashi (J Math Anal Appl 331:506-515, 2007), P.E.Maing $\acute{e}$ (Computers and Mathematics with Applications, 59: 74-79,2010) and other results in this field.

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References

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