New classification of analytic functions with negative coefficients

Abstract

New classification of analytic functions with negative coefficients is given by using the coefficients inequality, that is, new subclass A(p,n,Bk) of analytic functions with negative coefficient is defined. The object of the present paper is to prove various distortion theorems for functions in A(p,n,Bk), and for fractional calculus of functions belonging to A(p,n,Bk). Further, some properties of the class A(p,n,Bk) are shown.

Keywords

• analytic function
• distortion theorem
• fractional integral
• fractional derivative
• extreme point.