In this paper we study the linear openness of the composition of set-valued maps carried out thanks to applications of Nadler's fixed point theorem and Lim's lemma. As a byproduct, we obtain the Lipschitz property of the solution map of a generalized parametric equation and of parametric approximate variational inequalities, as well.
Bianchi, M., Kassay, G., Pini, R., Linear openness of the composition of set-valued maps and applications to variational systems, <<SET-VALUED AND VARIATIONAL ANALYSIS>>, 2016; (24): 581-595. [doi:10.1007/s11228-015-0357-0] [http://hdl.handle.net/10807/70010]
Linear openness of the composition of set-valued maps and applications to variational systems
Bianchi, Monica;Pini, Rita
2015
Abstract
In this paper we study the linear openness of the composition of set-valued maps carried out thanks to applications of Nadler's fixed point theorem and Lim's lemma. As a byproduct, we obtain the Lipschitz property of the solution map of a generalized parametric equation and of parametric approximate variational inequalities, as well.
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