# Viscosity regularization iterative methods and convergence analysis

Volume 10, Issue 11, pp 5712--5722 Publication Date: November 15, 2017       Article History
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### Authors

Dongfeng Li - School of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, China. Juan Zhao - School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.

### Abstract

In this paper, a Moudafi's type viscosity regularization iterative method is introduced and investigated for an $m$-accretive mapping and a nonexpansive mapping. Strong convergence of the regularization iterative method is obtained in the framework of real uniformly smooth Banach spaces. Some subresults are also provided as applications of the main results.

### Keywords

• Accretive mapping
• regularization iteration
• uniform smoothness
• operator equation

•  47H05
•  65J15
•  47N10

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