ON STRONGLY MIDCONVEX FUNCTIONS
By A. Azócar, J. Gimenez, Kazimierz Nikodem, J. Sánchez. 2011
53 citations recorded by the source corpus.
In this paper we collect some properties of strongly midconvex functions. First, counterparts of the classical theorems of Bernstein-Doetsch, Ostrowski and Sierpinski are presented. A version of Rode support theorem for strongly midconvex functions and a Kuhn-type result on the relation between strongly midconvex functions and strongly \(t\)-convex functions are obtained. Finally, a connection between strong midconvexity and generalized convexity in the sense of Beckenbach is established.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/17c6c67c04b9f8ce23555194a5a132980efc27ff
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Curvature of Feasible Sets in Offline and Online Optimization (2020, background): “More explicitly, since mid-point and regular strong convexity are equivalent for continuous functions [2], Lemma 1.”