East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS

  • He, Xin-Feng (College of Mathematics and Computer Hebei University) ;
  • Xu, Yong-Chun (Department of Mathematics Hebei North College) ;
  • He, Zhen (College of Mathematics and Computer Hebei University)
  • Received : 2010.01.13
  • Accepted : 2011.01.03
  • Published : 2011.01.31
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Abstract

In this paper, we consider an iterative scheme for finding a common element of the set of fixed points of a asymptotically quasi nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common fixed point of a asymptotically quasi-nonexpansive mapping and strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a asymptotically quasi-nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.

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References

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