Convex hulls and extreme points of families of starlike and close-to-convex mappings

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

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

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Harmonic Close-to-convex Mappings

Sufficient coefficient conditions for complex functions to be close-to-convex harmonic or convex harmonic are given. Construction of close-to-convex harmonic functions is also studied by looking at transforms of convex analytic functions. Finally, a convolution property for harmonic functions is discussed. Harmonic, Convex, Close-to-Convex, Univalent.

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

Distributions of Points and Large Convex Hulls of k Points

We consider a variant of Heilbronn’s triangle problem by asking for fixed integers d, k ≥ 2 and any integer n ≥ k for a distribution of n points in the d-dimensional unit cube [0, 1] such that the minimum volume of the convex hull of k points among these n points is as large as possible. We show that there exists a configuration of n points in [0, 1], such that, simultaneously for j = 2, . . . ...