SUFFICIENT CONDITIONS FOR STARLIKENESS OF RECIPROCAL ORDER

A normalized analytic function f defined on the unit disk D is starlike of reciprocal order alpha, 0 <= alpha < 1, if Re(f(z)/(zf'(z))) > alpha for all z is an element of D. Such functions are starlike and therefore univalent in D. Using the well-known MillerMocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order alpha. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f (z)/(zf'(z)) - 1| < 1 - alpha.