Applied Mathematics & Information Sciences

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In this paper, we introduce and investigate two subclasses H∗b(n,b,f ) and Kb (n,b,f ) of analytic functions with negative coefficients of order b in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(a), and convex K(a) of order a respectively. We also obtain the same coefficient inequalities and distortion theorem for such univalent functions with negative coefficients. We point out that the coefficient estimates up to z9 are enough to get the graphs of starlike and convex functions. Here in the sequel we give some examples, estimation and the graphical representation of such univalent functions by using the complex tool [8].

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