## Abstract and Applied Analysis

### Two-Step Viscosity Approximation Scheme for Variational Inequality in Banach Spaces

#### Abstract

This paper introduces and analyzes a viscosity iterative algorithm for an infinite family of nonexpansive mappings ${\{{T}_{i}\}}_{i=1}^{\infty }$ in the framework of a strictly convex and uniformly smooth Banach space. It is shown that the proposed iterative method converges strongly to a common fixed point of ${\{{T}_{i}\}}_{i=1}^{\infty }$, which solves specific variational inequalities. Necessary and sufficient convergence conditions of the iterative algorithm for an infinite family of nonexpansive mappings are given. Results shown in this paper represent an extension and refinement of the previously known results in this area.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 287602, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606041

Digital Object Identifier
doi:10.1155/2014/287602

Mathematical Reviews number (MathSciNet)
MR3191031

Zentralblatt MATH identifier
07022097

#### Citation

Yang, Liping; Kong, Weiming. Two-Step Viscosity Approximation Scheme for Variational Inequality in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 287602, 9 pages. doi:10.1155/2014/287602. https://projecteuclid.org/euclid.aaa/1412606041

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