## Tbilisi Mathematical Journal

### Certain subclasses of bi-univalent functions associated with the Chebyshev polynomials based on Hohlov operator

#### Abstract

In this paper we introduce and investigate two new subclasses of the function class $\Sigma$ biunivalent functions in the open unit disk, which are associated with the Hohlov operator, and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-MacLaurin coefficients $|a_2|$ and $|a_3|$ for functions in these new subclasses by using Chebyshev polynomials. Several new consequences of these results are also pointed out.

#### Note

The authors are grateful to the reviewers of this article, that gave valuable remarks, comments, and advices, in order to revise and improve the results of the paper.

#### Article information

Source
Tbilisi Math. J., Volume 11, Issue 2 (2018), 153-166.

Dates
Accepted: 2 April 2018
First available in Project Euclid: 6 July 2018

https://projecteuclid.org/euclid.tbilisi/1530842677

Digital Object Identifier
doi:10.32513/tbilisi/1530842677

Mathematical Reviews number (MathSciNet)
MR3954190

#### Citation

Murugusundaramoorthy, G.; Vijaya, K.; Güney, H. Ö. Certain subclasses of bi-univalent functions associated with the Chebyshev polynomials based on Hohlov operator. Tbilisi Math. J. 11 (2018), no. 2, 153--166. doi:10.32513/tbilisi/1530842677. https://projecteuclid.org/euclid.tbilisi/1530842677

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