Hugo LeivaNelson MerentesKazimierz NikodemJosé L. Sánchez2026-03-222026-03-22201310.1007/s10898-013-0051-4https://doi.org/10.1007/s10898-013-0051-4https://andeanlibrary.org/handle/123456789/48601Citaciones: 13We introduce the notion of strongly $$t$$ -convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly $$t$$ -convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representation is given. Finally, a connection between strongly convex set-valued maps and strongly convex sets is presented.enMathematicsConvex setAbsolutely convex setSubderivativeConvex analysisRegular polygonConnection (principal bundle)Convex combinationSet (abstract data type)Representation (politics)article