NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

doi:10.1007/s10473-019-0609-4

Abstract

Abstract: Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈ C:|z|<1}, normalized by the conditions f(0)=0 and f'(0)=1. Let U denote the set of all functions f ∈ A satisfying the condition
|(z/f(z))² f'(z) -1|<1 for z ∈ D.
Let Ω be the class of all f ∈ A for which
|zf'(z) -f(z)|<1/2, z ∈ D.
In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.

Key words: analytic, univalent, coefficient, Hadamard product

CLC Number:

30C45

Zhigang PENG, Milutin OBRADOVI?. NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS[J].Acta mathematica scientia,Series B, 2019, 39(6): 1579-1588.

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