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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- [4] Krishna, D.V., RamReddy, T., Coefficient inequality for a function whose derivative has a positive real part of order α, Math. Bohem., 140(2015), 43-52.
- [5] Krishna, D.V., Venkateswarlu, B., RamReddy, T., Third Hankel determinant for bounded turning functions of order alpha, J. Nigerian Math. Soc., 34(2015), 121-127.
- [6] MacGregor, T.H., Functions whose derivative has a positive real part, Trans. Amer. Math. Soc., 104(1962), 532-537.
- [7] Mocanu, P.T., Bulboaca, T., Salagean, G.S., Geometric Theory of Univalent Functions, (in romanian), House of the Book of Science, Cluj-Napoca, 2006.
- [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