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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 5
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Original Articles

Hybrid steepest-descent methods with a countable family of nonexpansive mappings for variational inequalities in Hilbert spaces

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Pages 953-964 | Received 13 Jul 2009, Accepted 27 Dec 2010, Published online: 15 Apr 2011
 

Abstract

Let H be a Hilbert space and let and be the countable families of nonexpansive mappings of H into itself such that . Assume that F is a nonlinear operator which is κ-Lipschitzian and η-strong monotone on C. In this article, we devise a new iterative scheme {x n } from an arbitrary initial point x 0H for the countable family of nonexpansive mappings and and prove that {x n } strongly converges to the unique solution x* of the variational inequality

Applications to constrained generalized pseudoinverse are included.

AMS Subject Classifications:

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