Summary:

*A. Moudafi* and

*P.-E. Maingé* [Fixed Point Theory Appl. 2006, Article ID 95453, 10 p. (2006;

Zbl 1143.47305)] and

*Xu* [Viscosity method for hierarchical fixed point approach to variational inequalities, Taiwanese J. Math. 13, No. 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

$\left({x}_{s,t}\right)$ of two parameters

$s,t\in (0,1)$, and under certain conditions, the iterated

${lim}_{t\to 0}{lim}_{s\to 0}{x}_{s,t}$ exists in the norm topology. Moudafi, Maingé and Xu stated the problem of convergence of

$\left({x}_{s,t}\right)$ as

$(s,t)\to (0,0)$ jointly in the norm topology. In this paper we further study the behaviour of the net

$\left({x}_{s,t}\right)$; in particular, we give a negative answer to this problem.