JIPAM logo: Home Link
Home Editors Submissions Reviews Volumes RGMIA About Us

  Volume 10, Issue 4, Article 98
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:


    Editors: Nak Eun Cho,  

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.

  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page

      search [advanced search] copyright 2003 terms and conditions login