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Chinese Journal of Mathematics
Volume 2014 (2014), Article ID 349719, 5 pages
http://dx.doi.org/10.1155/2014/349719
Research Article

A Few Inequalities Established by Using Fractional Calculus and Their Applications to Certain Multivalently Analytic Functions

Department of Mathematics, Faculty of Science, Çankırı Karatekin University, 18100 Çankırı, Turkey

Received 31 January 2014; Revised 11 June 2014; Accepted 11 June 2014; Published 18 June 2014

Academic Editor: Yifu Wang

Copyright © 2014 Hüseyin Irmak. 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.

Linked References

  1. P. L. Duren, Univalent Functions. Grundlehren der Mathematischen Wissenschaften 259, Springer, New York, NY, USA, 1983.
  2. M.-P. Chen, H. Irmak, and H. M. Srivastava, “Some families of multivalently analytic functions with negative coefficients,” Journal of Mathematical Analysis and Applications, vol. 214, no. 2, pp. 674–690, 1997. View at Google Scholar · View at Scopus
  3. A. W. Goodman, Univalent Functions. Vols. I and II, Polygonal Publishing House, Washington, NJ, USA, 1983.
  4. S. Owa, “On the distortion theorems I,” Kyungpook Mathematical Journal, vol. 18, pp. 53–59, 1978. View at Google Scholar
  5. H. Irmak and N. Tuneski, “Fractional calculus operator and certain applications in geometric function theory,” Sarajevo Journal of Mathematics, vol. 6, no. 18, pp. 51–57, 2010. View at Google Scholar
  6. H. Irmak and Ö. F. Çetin, “Some theorems involving inequalities on p-valent functions,” Turkish Journal of Mathematics, vol. 23, no. 3, pp. 453–459, 1999. View at Google Scholar · View at Scopus
  7. I. S. Jack, “Functions starlike and convex of order,” Journal of the London Mathematical Society, vol. 3, pp. 469–474, 1971. View at Google Scholar
  8. S. S. Miller and P. T. Mocanu, Dierential Subordinations, Theory and Applications, Marcel Dekker, New York, NY, USA, 2000.
  9. H. Irmak and N. E. Cho, “A dierential operator and its applications to certain multivalently analytic functions,” Hacettepe Journal of Mathematics and Statistics, vol. 36, no. 1, pp. 1–6, 2007. View at Google Scholar
  10. H. Irmak and M. Şan, “Some relations between certain inequalities concerning analytic and univalent functions,” Applied Mathematics Letters, vol. 23, no. 8, pp. 897–901, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. H. Irmak, T. Bulboacǎ, and N. Tuneski, “Some relations between certain classes consisting of α-convex type and Bazilevi type functions,” Applied Mathematics Letters, vol. 24, no. 12, pp. 2010–2014, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Irmak, “Certain inequalities and their applications to multivalently analytic functions,” Mathematical Inequalities and Applications, vol. 8, no. 3, pp. 451–458, 2005. View at Google Scholar · View at Scopus
  13. H. Irmak, “Certain inequalities and their applications to multtvalently analytic functions-II,” Mathematical Inequalities and Applications, vol. 13, no. 4, pp. 859–865, 2010. View at Google Scholar · View at Scopus