Stability results for Ekeland's ε variational principle for vector valued functions

In this paper, under the assumption that the nonconvex vector valued function f satisfies some lower semicontinuity property and bounded below, the nonconvex vector valued function sequence f <Subscript> n </Subscript> satisfies the same lower semicontinuity property and uniformly bounded below, and f <Subscript> n </Subscript> converges to f in the generalized sense of Mosco, we obtain the relation: <InlineEquation ID="Equ1"> <EquationSource Format="TEX"/> </InlineEquation>, when <InlineEquation ID="Equ2"> <EquationSource Format="TEX"/> </InlineEquation>, where <InlineEquation ID="Equ3"> <EquationSource Format="TEX"/> </InlineEquation> when <InlineEquation ID="Equ4"> <EquationSource Format="TEX"/> </InlineEquation>, C is the pointed closed convex dominating cone with nonempty interior int C, e∈int C. Under some conditions, we also prove the same result when f <Subscript> n </Subscript> converges to f in the generalized sense of Painleve'-Kuratowski. Copyright Springer-Verlag Berlin Heidelberg 1998