Cardinali, Tiziana; Nikodem, Kazimierz; Papalini, Francesca Some results on stability and on characterization of \(K\)-convexity of set-valued functions. (English) Zbl 0786.26016 Ann. Pol. Math. 58, No. 2, 185-192 (1993). The aim of this note is twofold. First, it is proved that the \(K\)- convexity of nonempty set-valued functions (in the finite-dimensional setting) is stable in the sense of Hyers and Ulam. This result generalizes and extends most of the results known about the stability of convex functions.The second goal is the characterization of nonempty compact set-valued \(K\)-convex functions in terms of \(K\)-\(t\)-convexity and \(K\)- quasiconvexity. Reviewer: Zs.Páles (Debrecen) Cited in 1 ReviewCited in 13 Documents MSC: 26E25 Set-valued functions 26B25 Convexity of real functions of several variables, generalizations 54C60 Set-valued maps in general topology Keywords:\(K\)-convexity; set-valued functions; stability of convex functions; \(K\)- quasiconvexity PDFBibTeX XMLCite \textit{T. Cardinali} et al., Ann. Pol. Math. 58, No. 2, 185--192 (1993; Zbl 0786.26016) Full Text: DOI