## Abstract and Applied Analysis

### Stable Perturbed Iterative Algorithms for Solving New General Systems of Nonlinear Generalized Variational Inclusion in Banach Spaces

#### Abstract

We introduce and study a new general system of nonlinear variational inclusions involving generalized $m$-accretive mappings in Banach space. By using the resolvent operator technique associated with generalized $m$-accretive mappings due to Huang and Fang, we prove the existence theorem of the solution for this variational inclusion system in uniformly smooth Banach space, and discuss convergence and stability of a class of new perturbed iterative algorithms for solving the inclusion system in Banach spaces. Our results presented in this paper may be viewed as an refinement and improvement of the previously known results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 659870, 11 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425048203

Digital Object Identifier
doi:10.1155/2014/659870

Mathematical Reviews number (MathSciNet)
MR3272207

Zentralblatt MATH identifier
07022843

#### Citation

Xiong, Ting-jian; Lan, Heng-you. Stable Perturbed Iterative Algorithms for Solving New General Systems of Nonlinear Generalized Variational Inclusion in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 659870, 11 pages. doi:10.1155/2014/659870. https://projecteuclid.org/euclid.aaa/1425048203

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