Spherically symmetric functions with a convex second derivative and applications to extremal probabilistic problems

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Three Extremal Problems for Hyperbolically Convex Functions

In this paper we apply a variational method to three extremal problems for hyperbolically convex functions posed by Ma and Minda and Pommerenke [7, 16]. We first consider the problem of extremizing Re f(z) z . We determine the minimal value and give a new proof of the maximal value previously determined by Ma and Minda. We also describe the geometry of the hyperbolically convex functions f(z) =...

Extremal Problems for a Class of Symmetric Functions

Since then, many extremal problems for the class ~ and related classes have been considered ([1], [2], [4] to [9]). In many of these extremal problems, the extremal function is symmetric with respect to the real axis; or if an extremal function is not unique, there exists a symmetric extremal function [7]. This leads us to consider the compact subclass of functions whose image is symmetric with...

some properties of certain subclasses of close-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points

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some properties of certain subclasses of close-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points