In this paper we discuss about normalized holomorphic functions whose derivatives have positive real part. For this class of functions, denoted R, we present a general distortion result (some upper bounds for the modulus of the kth derivative of a function). We present also some remarks on the functions whose derivatives have positive real part of order α, α ∈ (0, 1). More details about these classes of functions can be found in [6], [8], [7, Chapter 4] and [4]. In the last part of this paper we present two new subclasses of normalized holomorphic functions whose derivatives have positive real part which generalize the classes R and R(α). For these classes we present some general results and examples.
On some classes of holomorphic functions whose derivatives have positive real part
Abstract
Authors
Eduard Ștefan Grigoriciuc
Faculty of Mathematics and Computer Science, “Babeș-Bolyai” University, Cluj-Napoca, Romania
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Keywords
Univalent function, positive real part, distortion result, coefficient estimates
Paper coordinates
E.S. Grigoriciuc, On some classes of holomorphic functions whose derivatives have positive real part, Stud. Univ. Babeș-Bolyai Math. 66 (2021), No. 3, 479-490
References
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About this paper
Journal
Studia Mathematica
Publisher Name
Univ. Babes-Bolyai Math.
DOI
10.24193/subbmath.2021.3.06
Print ISSN
0252-1938
Online ISSN
2065-961x