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We introduce the subclass Tj(n,m,α) of analytic functions with negative coefficients by the operator Dn . Coefficient inequalities and distortion theorems of functions in Tj(n,m,α) are determind. Further, distortion theorems for fractional calculus of functions in Tj(n,m,α) are obtained.

Let 풮*(p,α) be the class of functions f(z) which are analytic and p-valently starlike of order α in the open unit disk E. The object of the present paper is to derive an interesting condition for f(z) to be in the class 풮*(p,α).

The object of the present paper is to show the extreme points of the class A(n,Bk) consisting of analytic functions with negative coefficients and the support points of the subclass A *(n,Bk) of A(n,Bk).

We introduce the subclass Tj(n,m,α) of analytic functions with negative coefficients by the operator Dn. Coefficient inequalities and distortion theorems of functions in Tj(n,m,α) are determind. Further, distortion theorems for fractional calculus of functions in Tj(n,m,α) are obtained.