Coefficient Estimates for Certain Subclasses of Analytic and Bi-univalent Functions

For lambda >= 0 and 0 <= alpha < beta, we denote by K(lambda; alpha, beta) the class of normalized analytic functions satisfying the two sided-inequality alpha < R (zf'(z)/f(z) + lambda z(2)f ''(z)/f(z)) < beta (z is an element of U) where U is the open unit disk. Let K-Sigma(lambda; alpha, beta) be the class of bi- univalent functions such that f and its inverse f(-1) both belong to the class K(lambda; alpha, beta) . In this paper, we establish bounds for the coefficients, and solve the Fekete-Szego problem, for the class K(lambda; alpha, beta) . Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coefficients of the functions in the class K-Sigma(lambda; alpha, beta).