# Successive coefficients for spirallike and related functions

## TL;DR

This paper investigates the bounds on the differences of successive coefficients in certain classes of univalent functions, including spirallike, starlike, and convex functions, within the unit disk.

## Contribution

It provides new estimates for the differences of successive coefficients for $eta$-spirallike functions of order $ heta$, extending known results to broader classes.

## Key findings

- Derived bounds for coefficient differences in $eta$-spirallike functions.
- Special cases include starlike and convex functions of order $ heta$.
- Results contribute to the understanding of coefficient behavior in geometric function theory.

## Abstract

We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\big | |a_{n+1}|-|a_n|\big |$, 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.