On some classes of holomorphic functions whose derivatives have positive real part

Abstract

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.

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

 

DOI: http://dx.doi.org/10.24193/subbmath.2021.3.06

References

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  • [8] Thomas, D.K., On functions whose derivative has positive real part, Proc. Amer. Math. Soc., 98(1986), 68-70.

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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