Open Access

On Janowski Starlike Functions

Journal of Inequalities and Applications20082007:014630

DOI: 10.1155/2007/14630

Received: 23 June 2007

Accepted: 3 October 2007

Published: 3 January 2008

Abstract

For analytic functions in the open unit disc with and , applying the fractional calculus for , a new fractional operator is introduced. Further, a new subclass consisting of associated with Janowski function is defined. The objective of the present paper is to discuss some interesting properties of the class .

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Authors’ Affiliations

(1)
Department of Mathematics and Computer Science, TC İstanbul Kültür University
(2)
Department of Mathematics, Kinki University

References

  1. Janowski W: Some extremal problems for certain families of analytic functions. I. Annales Polonici Mathematici 1973, 28: 297–326.MathSciNetMATHGoogle Scholar
  2. Owa S: Univalent and Geometric Function Theory Seminar Notes. TC İstanbul Kültür University, İstanbul, Turkey; 2006.Google Scholar
  3. Owa S: On the distortion theorems. I. Kyungpook Mathematical Journal 1978,18(1):53–59.MathSciNetMATHGoogle Scholar
  4. Srivastava HM, Owa S (Eds): Univalent Functions, Fractional Calculus, and Their Applications, Ellis Horwood Series: Mathematics and Its Applications. Ellis Horwood, Chichester, UK; 1989:404.Google Scholar
  5. Goodman AW: Univalent Functions. Vol. I. Mariner, Tampa, Fla, USA; 1983:xvii+246.MATHGoogle Scholar
  6. Jack IS: Functions starlike and convex of order. Journal of the London Mathematical Society 1971, 3: 469–474. 10.1112/jlms/s2-3.3.469MathSciNetView ArticleMATHGoogle Scholar
  7. Miller SS, Mocanu PT: Differential Subordinations. Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 225. Marcel Dekker, New York, NY, USA; 2000:xii+459.Google Scholar
  8. Aouf MK: On a class of-valent starlike functions of order. International Journal of Mathematics and Mathematical Sciences 1987,10(4):733–744. 10.1155/S0161171287000838MathSciNetView ArticleMATHGoogle Scholar

Copyright

© M. Çag̃lar et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.