Viscosity approximation methods with a sequence of contractions

Koji Aoyama; Yasunori Kimura

doi:10.4067/S0719-06462014000100002

Authors

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.

DOI:

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

Keywords:

Viscosity approximation method, nonexpansive mapping, fixed point, hybrid steepest descent method

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.