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Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions

Abstract: In this paper, we introduce and investigate two new subclasses H-sigma(mu) (lambda,phi) and M-sigma(gamma) (lambda, mu, phi) of Ma-Minda bi-univalent functions defined by using subordination in the open unit disk D = {z is an element of C : vertical bar z vertical bar < 1}. For functions belonging to these new subclasses, we obtain estimates for the initial coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar. The results presented in this paper would generalize those in related works of several earlier authors.
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