Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A CONVERGENCE THEOREM ON QUASI-ϕ-NONEXPANSIVE MAPPINGS

  • Kang, Shin Min (Department of Mathematics and the RINS Gyeongsang National University) ;
  • Cho, Sun Young (Department of Mathematics Gyeongsang National University) ;
  • Kwun, Young Chel (Department of Mathematics Dong-A University) ;
  • Qin, Xiaolong (Department of Mathematics Gyeongsang National University)
  • Received : 2009.10.29
  • Accepted : 2010.01.18
  • Published : 2010.03.30
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Abstract

In an infinite-dimensional Hilbert space, the normal Mann iteration has only weak convergence, in general, even for nonexpansive mappings. The purpose of this paper is to modify the normal Mann iteration to have strong convergence for a closed quasi-$\phi$-nonexpansive mapping in the framework of Banach spaces.

Keywords

Acknowledgement

Supported by : Dong-A University

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