Successive coefficients for spirallike and related functions

Abstract

We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2{z}^2+a_3{z}^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $||a_{n+1}|-|a_n||$, for $f$ belonging to the family of $\gamma$-spirallike functions of order $\alpha$. Our particular results include the case of starlike and convex functions of order $\alpha$ and other related class of functions.

12 pages, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM. To appear