Characterization of certain fractional-type set-valued functions

In this paper, we give some characterizations of a special class of fractional-type set-valued functions in terms of convexity-preserving properties of sets by direct and inverse images. We begin by generalizing the so-called ratios of affine functions, initially introduced by Rothblum, to set-valued functions by using an affinity concept introduced in the literature by Gorokhovik. Next, we investigate some convexity properties for general fractional-type set-valued functions and provide a series of convexity-preserving results of sets under set-valued ratios of affine functions.