Coefficient inequalities for certain analytic functions

For real α(α > 1), we introduce subclasses M(α) and N(α) of analytic functions f(z) with f(0) = 0 and f′(0) = 1 in U. The object of the present paper is to consider the coefficient inequalities for functions f(z) to be in the classes M(α) and N(α). Further, the bounds of α for functions f(z) to be starlike in U are considered.