Abstract

Let 𝒜 denote the class of analytic functions in the unit disk 𝔻:={z∈ℂ:|z|<1} satisfying f(0)=0 and f ′ (0)=1. Let 𝒰 be the class of functions f∈𝒜 satisfying

Highlights

  • Introduction and PreliminariesLet H denote the class of analytic functions in the unit disk D := {z ∈ C : |z| < 1}

  • A set D ⊂ C is said to be starlike with respect to a point z0 ∈ D if the line segment joining z0 to every other point z ∈ D lies entirely in D

  • Be the class of close-to-convex functions. It is well-known that every close-to-convex function is univalent in D

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Summary

Introduction and Preliminaries

Let H denote the class of analytic functions in the unit disk D := {z ∈ C : |z| < 1}. Denote by S ∗ and C the classes of starlike and convex functions in S respectively. It is well-known that a function f ∈ A belongs to. It is well-known that every close-to-convex function is univalent in D. The Krein–Milman theorem [9] asserts that every compact subset of a locally convex topological vector space is contained in the closed convex hull of its extreme points. A function f is called support point of a compact subset F of H if f ∈ F , and if there is a continuous linear functional J on H such that Re J is non-constant on F , and. The main aim of this paper is to characterize the set of support points of the classes U and G

Support points of the class U
Support points of the class G
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