Malaysian Journal of Mathematical Sciences, May 2017, Vol. 11, No. 2
Faber Polynomial Coefficient Estimates for Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Fractional Derivative
Sakar, F. M. and Güney, H. O.
Corresponding Email: mugesakar@hotmail.com
Received date: 17 January 2017
Accepted date: 7 March 2017
Abstract:
A new subclass of bi-univalent functions both \(f\) and \(f^{-1}\) which are mfold symmetric analytic functions are investigated in this study. We also determine the estimate for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, using the Faber polynomial expansion, upper bounds of \(|a_{m+1}|\), \(|a_{2m+1}|\), and \(|a_{m+1}^{2}-a_{2m+1}|\) coefficients for analytic bi-univalent functions defined by fractional calculus are found in this study.
Keywords: Univalent function, fractional operator, m-fold symmetric, Faber polynomial
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