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The aim of this note is twofold: first, to show that arcwise connected cone-quasiconvex set-valued mappings can be characterized in terms of classical arcwise connected quasiconvexity of certain real-valued functions, defined by Gerstewitz’s scalarization function; second, by making use of the recent result concerning the Pareto reducibility in multicriteria arcwise connected cone-quasiconvex optimization problems to establish similar set-valued optimization problems under appropriate assumptions.

Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization