Hybrid Steepest-Descent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators. (24th January 2010)

• Record Type: Journal Article
• Authors: He, Songnian; Liang, Xiao-Lan
• Other Names: Suzuki Tomonari Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2010-01-24
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/673932
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : Let H be a real Hilbert space and let F : H → H be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality V I ( C, F ) of finding a point x ∗ ∈ C such that 〈 F x ∗, x − x ∗ 〉 ≥ 0, for all x ∈ C, where C is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudocontractions. Strong convergence of the algorithms is proved.