GENERALIZATIONS OF HADAMARD-PRODUCTS OF FUNCTIONS WITH NEGATIVE COEFFICIENTS

Let T(n) be the class of functions with negative coefficients which ar e analytic in the unit disk U For functions f(1)(z) and f(2)(z) belong ing to T(n), generalizations of the Hadamard product of f(1)(z) and f( 2)(z) represented by (f(1) Delta f(2))(p, q; z) are introduced. In the present paper, some interesting properties of these generalizations o f Hadamard products of functions in T(n, alpha) and C(n, alpha) are g iven. (C) 1996 Academic Press, Inc.