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Abstract

The purpose of this paper is two-fold. Firstly, we present two general stability theorems for extended real-valued variational inequalities and for extended real-valued hemivariational inequalities, respectively. As a main novelty of this paper, both these theorems cover stability with respect to extended real-valued convex lower semicontinuous functions, and not only stability with respect to linear forms in variational inequalities and in hemivariational inequalities, respectively. Secondly, we derive from these theorems new stability results for various variational problems. Namely we deal with a class of mixed variational inequalities involving random convex functionals, random linear forms and random constraint sets and give a stability result with respect to these data. Then we turn to hemivariational inequalities. We study a scalar bilateral obstacle problem with unilateral and non-monotone boundary conditions and provide a stability result with respect to the obstacles. Finally we are concerned with frictionless unilateral contact problems with locking material in linear elasticity and discuss the issue of stability with respect to the locking constraint.