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The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Sãlãgean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients a2 and a3 and upper bounds for the Fekete-Szegö functional for the functions in this class. The results proved by various authors follow as particular cases.

This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients |a2| and |a3| for the functions in these classes. Also we investigate upper bounds for the Fekete-Szegö functional and second Hankel determinant for these classes.

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In this present investigation a subclass of alpha convex bi-univalent functions of complex order in the open unit disc U = {z :| z |< 1}, defined by Salagean operator and quasi- subordination is discussed. The estimates on the initial coefficients |a 2 | and |a 3 | for the functions in this subclass are studied. The results obtained in this paper would generalise those already proved by various authors.