On new classes of analytic functions with negative coefficients

Abstract

We introduce the classes Kn* of analytic functions with negative coefficients by using the nth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functions f(z) in Kn*. Further we consider the modified Hadamard product of functions fi(z) in Kni*(n=1,2,…,m).