On The Convergence Of An Iteration Process For Totally Asymptotically I-Nonexpansive Mappings

Authors

  • Birol GUNDUZ Erzincan University
  • Sezgin AKBULUT Ataturk University

Abstract

Suppose that K be a nonempty closed convex subset of a real Banach space X and T,S:K???K be two totally asymptotically I-nonexpansive mappings, where I:K???K is a totally asymptotically nonexpansive mapping. We define the iterative??sequence {x_{n}} by
{<K1.1/>,n??????,???
<K1.1 ilk="MATRIX" >x??????Kx_{n+1}=(1-??_{n})x_{n}+??_{n}S??y_{n}y_{n}=(1-??_{n})x_{n}+??_{n}T??z_{n}z_{n}=(1-??_{n})x_{n}+??_{n}I??x_{n}</K1.1>where {??_{n}},{??_{n}} ve {??_{n}} are sequences in [0,1].Under some suitable conditions, the strong and weak convergence theorems of {x_{n}} to a common fixed point of S,T and I are obtained.

Author Biographies

Birol GUNDUZ, Erzincan University

Department of Mathematics, Faculty of Science and Art, Erzincan University, Erzincan, 24000, Turkey.

Sezgin AKBULUT, Ataturk University

Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey.

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Published

2016-12-20

How to Cite

GUNDUZ, B., & AKBULUT, S. (2016). On The Convergence Of An Iteration Process For Totally Asymptotically I-Nonexpansive Mappings. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 7(1), 17-30. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/403

Issue

Section

Research Article