On relaxed viscosity iterative methods for variational inequalities in Banach spaces

On relaxed viscosity iterative methods for variational inequalities in Banach spaces In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

On relaxed viscosity iterative methods for variational inequalities in Banach spaces

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Publisher
Elsevier
Copyright
Copyright © 2009 Elsevier B.V.
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/j.cam.2009.01.015
Publisher site
See Article on Publisher Site

Abstract

In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 15, 2009

References

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