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On strongly midconvex functions

Azocar A., Gimenez J., Nikodem K., Sanchez J. L.

Opuscula Mathematica

2011

Vol. 31, no. 1

15-26

In this paper we collect some properties of strongly midconvex functions. First, counterparts of the classical theorems of Bernstein-Doetsch, Ostrowski and Sierpiński are presented. A version of Rod é 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

Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

Azocar A., Guerrero J. A., Matkowski J., Merentes N.

Opuscula Mathematica

2010

Vol. 30, no. 1

53-60

We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.