In this paper, under the assumption that the nonconvex vector valued function f satisfies some lower semicontinuity property and is bounded below, the nonconvex vector valued function sequence fn satisfies the same lower semicontinuity property is and uniformly bounded below, and fn converges to f in the generalized sense of Mosco, we obtain the relation: √(ϵ) – ext f = {&xmacr; : f(x) – f(&xmacr;) + √(ϵ)‖x – &xmacr;‖e ∉ – C, when x ≠ &xmacr;} ⊆ limn→∞ √(ϵ) – ext fn, where √(ϵ)-ext fn = {&xmacr; : fn(x) – fn(&xmacr;) + √(ϵ)‖x – &xmacr;‖e ∉ – C, when x ≠ &xmacr;}, 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.
