JIPAM

An Application of Hölder's Inequality for Convolutions  
 
  Authors: Junichi Nishiwaki, Shigeyoshi Owa,  
  Keywords: Analytic function, Multivalent starlike, Multivalent convex.  
  Date Received: 30/03/2009  
  Date Accepted: 16/07/2009  
  Subject Codes:

30C45.

  
  Editors: Nak Eun Cho,  
 
  Abstract:

Let $ mathcal{A}_p(n)$ be the class of analytic and multivalent functions $f(z)$ in the open unit disk $ mathbb{U}$. Furthermore, let $ mathcal{S}_p(n, alpha)$ and $ mathcal{T}_p(n, alpha)$ be the subclasses of $ mathcal{A}_p(n)$ consisting of multivalent starlike functions $f(z)$ of order $ alpha$ and multivalent convex functions $f(z)$ of order $ alpha$, respectively. Using the coefficient inequalities for $f(z)$ to be in $ mathcal{S}_p(n, alpha)$ and $ mathcal{T}_p(n, alpha)$, new subclasses $ mathcal{S}_p^*(n, alpha)$ and $ mathcal{T}_p^*(n, alpha)$ are introduced. Applying the Hölder inequality, some interesting properties of generalizations of convolutions (or Hadamard products) for functions $f(z)$ in the classes $ mathcal{S}_p^*(n, alpha)$ and $ mathcal{T}_p^*(n, alpha)$ are considered. ;


This article was printed from JIPAM
http://jipam.vu.edu.au

The URL for this article is:
http://jipam.vu.edu.au/article.php?sid=1154