Displaying similar documents to “k-convexity in several complex variables”

Delta-convex mappings between Banach spaces and applications

L. L. Veselý, L. Zajíček

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We investigate delta-convex mappings between normed linear spaces. They provide a generalization of functions which are representable as a difference of two convex functions (labelled as 5-convex or d.c. functions) and are considered in many articles. We show that delta-convex mappings have many good differentiability properties of convex functions and the class of them is very stable. For example, the class of locally delta-convex mappings is closed under superpositions and (in some...

Convex combination of analytic functions

Nak Eun Cho, Naveen Kumar Jain, V. Ravichandran (2017)

Open Mathematics

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Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).