In this paper some concepts and techniques of Mathematical Programming are extended in an intrinsic way from the Euclidean space to the sphere. In particular, the notion of convex functions, variational problem and monotone vector fields are extended to the sphere and several characterizations...

We introduce the notion of strongly <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$t$$</EquationSource> </InlineEquation>-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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$t$$</EquationSource> </InlineEquation>-convex...</equationsource></inlineequation></equationsource></inlineequation>

In this technical note we give a short proof based on standard results in convex analysis of some important characterization results listed in Theorem 3 and 4 of [1]. Actually our result is slightly general since we do not specify the convex set X. For clarity we use the same notation for the...

In this technical note we give a short proof based on standard results in convex analysis of some important characterization results listed in Theorem 3 and 4 of [1]. Actually our result is slightly general since we do not specify the convex set X. For clarity we use the same notation for the...

AMS classifications: 62G05; 62G07; 62G08; 62G20; 62G32;