Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods

Nguyen Buong () and Nguyen Thi Hong Phuong ()
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Nguyen Buong: VAST
Nguyen Thi Hong Phuong: VAST

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 2, No 6, 399-411

Abstract: Abstract In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. Their strong convergence is proved, by using new V-mappings instead of W-ones.

Keywords: Nonexpansive mapping; Fixed point; Variational inequality (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-013-0350-4

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