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

Abstract

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 fn satisfies the same lower semicontinuity property and uniformly bounded below, and fn converges to f in the generalized sense of Mosco, we obtain the relation: \(\), when \(\), where \(\)when\(\), 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 fn converges to f in the generalized sense of Painleve'-Kuratowski.