Abstract
In this paper our main aim is to give some su¢ cient conditions for functions represented with normalized Wright functions to be univalent in the open unit disk. The key tools in our proofs are the Beckerís and the generalized version of the well-known Ahlforís and Beckerís univalence criteria.
Highlights
Let A be the class of analytic functionsf (z) in the open unit disk U = fz 2 C : jzj < 1g, normalized by f (0) = 0 = f 0(0) 1 of the form f (z) = z + a2z2 + a3z3 + + anzn + X 1 = z + anzn: (1.1) n=2It is well-known that a function f : C ! C is said to be univalent if the following condition is satis...ed: z1 = z2 iff (z1) = f (z2)
In this paper our main aim is to give some su¢ cient conditions for functions represented with normalized Wright functions to be univalent in the open unit disk
We denote by S the subclass of A consisting of functions which are univalent in U
Summary
It is well-known that a function f : C ! C is said to be univalent if the following condition is satis...ed: z1 = z2 iff (z1) = f (z2). We denote by S the subclass of A consisting of functions which are univalent in U. For some recent investigations of various subclasses of the univalent functions class S, see the works by Altintas et al [1], Gao et al [7], and Owa et al [8]. In recent years there have been many studies (see for example [2,3,4,5,6, 9, 10]) on the univalence of the following integral operators: Zz
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