Tbilisi Mathematical Journal

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

G. Murugusundaramoorthy, K. Vijaya, and H. Ö. Güney

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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
Received: 6 October 2017
Accepted: 2 April 2018
First available in Project Euclid: 6 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1530842677

Digital Object Identifier
doi:10.32513/tbilisi/1530842677

Mathematical Reviews number (MathSciNet)
MR3954190

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C50: Coefficient problems for univalent and multivalent functions

Keywords
Analytic functions bi-univalent functions Chebyshev polynomials coefficient estimates

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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