✦ LIBER ✦

On relaxed viscosity iterative methods for variational inequalities in Banach spaces

✍ Scribed by L.-C. Ceng; Q.H. Ansari; J.C. Yao

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 635 KB
Volume: 230
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.01.015

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✦ Synopsis

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.

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