An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,...An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re {eiδ(1-z)2f′(z)} 〉 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.展开更多
Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2)...Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/hα(z)} 〉 0, z ∈ D. For the class l(hα) of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.展开更多
文摘An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re {eiδ(1-z)2f′(z)} 〉 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
文摘Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/hα(z)} 〉 0, z ∈ D. For the class l(hα) of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.