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.
Zhigang PENG
,
Milutin OBRADOVI?
. NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS[J]. Acta mathematica scientia, Series B, 2019
, 39(6)
: 1579
-1588
.
DOI: 10.1007/s10473-019-0609-4
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