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- Title
ON AN IMPLICIT HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES.
- Authors
Cianciaruso, Filomena; Colao, Vittorio; Muglia, Luigi; Hong-Kun Xu
- Abstract
Moudafi and Maingé [Towards viscosity approximations of hierarchical fixed-point problems, Fixed Point Theory Appl. (2006), Art. ID 95453, 10pp] and Xu [Viscosity method for hierarchical fixed point approach to variational inequalities, Taiwanese J. Math. 13(6) (2009)] studied an implicit viscosity method for approximating solutions of variational inequalities by solving hierarchical fixed point problems. The approximate solutions are a net (xs,t) of two parameters s, t ϵ (0, 1), and under certain conditions, the iterated limt→0 lims→0 xs,t exists in the norm topology. Moudafi, Maingé and Xu stated the problem of convergence of (xs,t) as (s, t) → (0, 0) jointly in the norm topology. In this paper we further study the behaviour of the net (xs,t); in particular, we give a negative answer to this problem.
- Subjects
FIXED point theory; VARIATIONAL inequalities (Mathematics); VISCOSITY solutions; ALGEBRAIC functions; NONEXPANSIVE mappings; ACCELERATION of convergence in numerical analysis
- Publication
Bulletin of the Australian Mathematical Society, 2009, Vol 80, Issue 1, p117
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972709000082