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

Let𝒮*(p,α)be the class of functionsf(z)which are analytic andp-valently starlike of orderαin the open unit diskE. The object of the present paper is to derive an interesting condition forf(z)to be in the class𝒮*(p,α).

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