In this research article, we study a bi-univalent subclass Σ related with Faber polynomial and investigate the coefficient estimate |an| for functions in the considered subclass with a gap series condition. Also, we obtain the initial two coefficient estimates |a2|, |a3| and find the Fekete–Szegö functional |a3−a22| for the considered subclass. New results which are further examined are also pointed out in this article. © 2018, Springer Nature Switzerland AG.

Janani T

Department of Database Systems

School of Computer Science and Engineering

Vellore Campus

Yalcin S.

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Coefficient Bounds of Bi-univalent Functions Using Faber Polynomial

Trends in Mathematics Advances in Algebra and Analysis

We define a new class of meromorphic bi-univalent functions and use the Faber polynomial expansions to determine the coefficient bounds for such functions. Our results generalize and/or improve some of the previously known results. A meromorphic function is said to be bi-univalent in a given domain δ if both the function and its inverse map are univalent there. Nous définissons une nouvelle classe de fonctions méromorphes bi-univalentes et utilisons des développements en polynÔmes de Faber pour déterminer des bornes sur les coefficients de ces fonctions. Nos résultats généralisent et améliorent certains résultats antérieurement connus. Une fonction méromorphe est dite ici être bi-univalente dans un domaine donné δ si la fonction et sa fonction réciproques y sont toutes deux univalentes. © 2014 Académie des sciences.

Comptes Rendus Mathematique

Coefficient estimates for certain classes of meromorphic bi-univalent functions

Journal of Complex Analysis

Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh q-Differential Operator

Faber polynomial coefficient bounds for a subclass of bi-univalent functions

Coefficient estimates for a class of meromorphic bi-univalent functions

Filomat

Coefficient estimates for a general subclass of analytic and bi-univalent functions

Journal	Data powered by TypesetTrends in Mathematics Advances in Algebra and Analysis
Publisher	Data powered by TypesetSpringer International Publishing
ISSN	2297-0215
Open Access	No