Viscosity approximation methods with a sequence of contractions

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DOI:

https://doi.org/10.4067/S0719-06462014000100002

Abstract

The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the viscosity approximation method with a sequence of contractions is convergent whenever so is every iterative sequence generated by the Halpern type iterative method. Then, using our results, we show some convergence theorems for variational inequality problems, zero point problems, and fixed point problems.

Keywords

Viscosity approximation method , nonexpansive mapping , fixed point , hybrid steepest descent method
  • Koji Aoyama Department of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan.
  • Yasunori Kimura Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan.
  • Pages: 09–20
  • Date Published: 2014-03-01
  • Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal

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Published

2014-03-01

How to Cite

[1]
K. Aoyama and Y. Kimura, “Viscosity approximation methods with a sequence of contractions”, CUBO, vol. 16, no. 1, pp. 09–20, Mar. 2014.

Issue

Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal

Section

Articles