A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces

• Main Authors: Wangkeeree Rabian, Kamraksa Uthai
• Format: Article
• Language: English
• Published: SpringerOpen 2009-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2009/369215

<p/> <p>We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of <inline-formula> <graphic file="1687-1812-2009-369215-i1.gif"/></inline-formula>-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008).</p>