BOUNDS FOR INITIAL MACLAURIN COEFFICIENTS FOR A NEW SUBCLASSES OF ANALYTIC AND M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

BOUNDS FOR INITIAL MACLAURIN COEFFICIENTS FOR A NEW SUBCLASSES OF ANALYTIC AND M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

A. K. Wanas

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Abstract

In the present paper, we introduce and study two new subclasses of the function class m consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. We establish upper bounds for the initial coecients jam+1j and ja2m+1j for functions in these subclasses. Certain special cases are also indicated.

Keywords

Analytic functions, univalent functions, bi-univalent functions, m-fold symmetric bi-univalent functions, coecient bounds.