Taiwanese Journal of Mathematics

VISCOSITY METHOD FOR HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES

Hong-Kun Xu

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Abstract

A viscosity method for a hierarchical fixed point approach to variational inequality problems is presented. This method is used to solve variational inequalities where the involving operators are complements of nonexpansive mappigs and the solutions are sought in the set of the fixed points of another nonexpansive mapping. Such variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 463-478.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405802

Digital Object Identifier
doi:10.11650/twjm/1500405802

Mathematical Reviews number (MathSciNet)
MR2655782

Zentralblatt MATH identifier
1215.47099

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
Secondary: 58E35: Variational inequalities (global problems) 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 65J25

Keywords
viscosity method variational inequality nonexpansive mapping iterative method hierarchical fixed point projection

Citation

Xu, Hong-Kun. VISCOSITY METHOD FOR HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES. Taiwanese J. Math. 14 (2010), no. 2, 463--478. doi:10.11650/twjm/1500405802. https://projecteuclid.org/euclid.twjm/1500405802


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