Abstract
Considering a function f(z)=z/1-z2 which is analytic and starlike in the open unit disc U and a function f(z)=z/1-z which is analytic and convex in U, we introduce two new classes Sα⁎(β) and Kα(β) concerning fα(z)=z/1-zα (α>0). The object of the present paper is to discuss some interesting properties for functions in the classes Sα⁎(β) and Kα(β).
Highlights
Introduction and PreliminariesLet A be the class of functions f(z) which are analytic in the open unit disk U = {z ∈ C : |z| < 1} with f(0) = 0 and f(0) = 1.Let S denote the subclass of A consisting of functions f(z) ∈ A which are univalent in U
U, we introduce two new classes S∗α(β) and Kα discuss some interesting properties for functionsthcoencclaesrsneisnSg ∗αf(αβ(z) )an=d z/(1 − zα) Kα(β)
Let S∗(β) be the subclass of S consisting of f(z) which are starlike of order β (0 ≤ β < 1) in U
Summary
Let A be the class of functions f(z) which are analytic in the open unit disk U = {z ∈ C : |z| < 1} with f(0) = 0 and f(0) = 1. Let S denote the subclass of A consisting of functions f(z) ∈ A which are univalent in U. Let S∗(β) be the subclass of S consisting of f(z) which are starlike of order β (0 ≤ β < 1) in U. Is in the class K(0) ≡ K. for some real α (0 < α ≤ 2), we discuss some properties between functions f(z) in (2) and (3), where we consider the principal value for znα. For some With real the β (0 ≤ above β < 1), we definitions for say the that f(z) ∈ classes S∗α
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