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International Journal of Differential Equations
Volume 2014, Article ID 458090, 6 pages
http://dx.doi.org/10.1155/2014/458090
Research Article

On Certain Class of Non-Bazilevič Functions of Order Defined by a Differential Subordination

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia

Received 29 April 2014; Revised 27 June 2014; Accepted 2 July 2014; Published 17 July 2014

Academic Editor: Salim Messaoudi

Copyright © 2014 A. G. Alamoush and M. Darus. 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. M. Obradović, “A class of univalent functions,” Hokkaido Mathematical Journal, vol. 27, no. 2, pp. 329–335, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Z. Wang, C. Gao, and M. Liao, “On certain generalized class of non-Bazilevič functions,” Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, vol. 21, no. 2, pp. 147–154, 2005. View at Google Scholar · View at MathSciNet
  3. N. Tuneski and M. Darus, “Fekete-Szegö functional for non-Bazilevic functions,” Acta Mathematica Academiae Paedagogicae Nyí regyháziensis, vol. 18, pp. 63–65, 2002. View at Google Scholar
  4. A. A. Amer and M. Darus, “Distortion theorem for certain class of Bazilevic functions,” International Journal of Mathematical Analysis, vol. 6, no. 9–12, pp. 591–597, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. W. Ibrahim and M. Darus, “Mixed class of functions of non-Bazilevic type and bounded turning,” Far East Journal of Mathematical Sciences, vol. 67, no. 1, pp. 141–152, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  6. R. W. Ibrahim and M. Darus, “Argument estimate for non-Bazilevic type and bounded turning functions,” Far East Journal of Mathematical Sciences, vol. 68, no. 2, pp. 175–183, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  7. R. W. Ibrahim, M. Darus, and N. Tuneski, “On subordination for classes of non-Bazilevic type,” Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia A, vol. 64, no. 2, pp. 49–60, 2010. View at Google Scholar
  8. M. Darus and R. W. Ibrahim, “On subclasses of uniformly Bazilevic type functions involving generalised differential and integral operators,” Far East Journal of Mathematical Sciences (FJMS), vol. 33, no. 3, pp. 401–411, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. N. Shanmugam, S. Sivasubramanian, M. Darus, and S. Kavitha, “On sandwich theorems for certain subclasses of non-Bazilevic functions involving Cho-Kim transformation,” Complex Variables and Elliptic Equations, vol. 52, no. 10-11, pp. 1017–1028, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” The Michigan Mathematical Journal, vol. 28, no. 2, pp. 157–172, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. S. Liu, “On a subclass of p-valent close-to-convex functions of order β and type α,” Journal of Mathematical Study, vol. 30, no. 1, pp. 102–104, 1997. View at Google Scholar · View at MathSciNet
  12. M.-S. Liu, “On certain class of analytic functions defined by differential subordination,” Acta Mathematica Scientia B, vol. 22, no. 3, pp. 388–392, 2002. View at Google Scholar · View at MathSciNet · View at Scopus
  13. W. Rogosinski, “On the coefficients of subordination functions,” Proceedings of the London Mathematical Society 2, vol. 48, pp. 48–82, 1943. View at Google Scholar
  14. R. Singh, “On Bazilevic functions,” Proceedings of the American Mathematical Society, vol. 38, pp. 261–271, 1973. View at Google Scholar · View at MathSciNet