Extremal Problems in the Class of Close-to-Convex Functions

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) =...

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

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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Extremal problems for convex polygons

Consider a convex polygon Vn with n sides, perimeter Pn, diameter Dn, area An, sum of distances between vertices Sn and widthWn. Minimizing or maximizing any of these quantities while fixing another defines ten pairs of extremal polygon problems (one of which usually has a trivial solution or no solution at all). We survey research on these problems, which uses geometrical reasoning increasingl...