Tbilisi Mathematical Journal

Coefficient estimates for a general subclass of $m$-fold symmetric bi-univalent functions

Ahmad Motamednezhad and Safa Salehian

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Abstract

In the present paper, we introduce and investigate an interesting subclass ${\mathcal B}_{{\Sigma}_m}^{h,p}(\lambda,\gamma)$ of $m$-fold symmetric bi-univalent functions in the open unit disk $\mathbb{U}$. Furthermore, we obtain estimates on the coefficients $|a_{m+1}|$ and $|a_{2m+1}|$ for functions belonging to this subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Note

We would like to thank the referee for carefully reading our manuscript.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 2 (2019), 163-176.

Dates
Received: 26 November 2018
Accepted: 7 May 2019
First available in Project Euclid: 21 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1561082575

Digital Object Identifier
doi:10.32513/tbilisi/1561082575

Mathematical Reviews number (MathSciNet)
MR3973267

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination

Keywords
univalent functions bi-univalent functions $m$-fold symmetric univalent functions $m$-fold symmetric bi-univalent functions coefficient estimates

Citation

Motamednezhad, Ahmad; Salehian, Safa. Coefficient estimates for a general subclass of $m$-fold symmetric bi-univalent functions. Tbilisi Math. J. 12 (2019), no. 2, 163--176. doi:10.32513/tbilisi/1561082575. https://projecteuclid.org/euclid.tbilisi/1561082575


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