On Lipschitz-like property for polyhedral moving sets

On Lipschitz-like continuity of a class of set-valued mappings

“…We generalize results from [25] and [3]. In [25] the respective results are obtained under stronger assumptions of functions h i , i ∈ I 0 ∪ I, while in [3] the Lipschitz-likeness of F is obtained for h i (p, x) = x | g i (p) − f i (p), i ∈ I 0 ∪ I, where f i : G → R, g i : G → H, i ∈ I 0 ∪ I, are locally Lipschitz functions. We also correct the mistake in the proof of Lemma 3 of [25].…”

“…Let us note that for some particular functions h i (•, •), i ∈ I ∪ I 0 Theorem 5.3 has been already proved in [3].…”

“…In [3] we discussed in details the proof of Lemma 3 of [25] for some special functions h i , i = 1, . .…”