East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A NEW GENERALIZED RESOLVENT AND APPLICATION IN BANACH MAPPINGS

  • Wang, Xian (College of Mathematics and Computer, Hebei University) ;
  • Chen, Jun-Min (College of Mathematics and Computer, Hebei University) ;
  • He, Zhen (College of Mathematics and Computer, Hebei University)
  • Received : 2013.05.15
  • Accepted : 2014.01.14
  • Published : 2014.01.31
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Abstract

In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.

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References

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