Displaying similar documents to “Extreme Points of Families of Analytic Functions Subordinate to Convex Mappings.”

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...

k-convexity in several complex variables

Hidetaka Hamada, Gabriela Kohr (2002)

Annales Polonici Mathematici

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We define and investigate the notion of k-convexity in the sense of Mejia-Minda for domains in ℂⁿ and also that of k-convex mappings on the Euclidean unit ball.

On a generalization of close-to-convex functions

Swadesh Kumar Sahoo, Navneet Lal Sharma (2015)

Annales Polonici Mathematici

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The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate...