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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 847287, 6 pages
http://dx.doi.org/10.1155/2013/847287
Research Article

Certain Properties of a Class of Close-to-Convex Functions Related to Conic Domains

Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan

Received 30 September 2012; Revised 3 March 2013; Accepted 17 March 2013

Academic Editor: Nikolaos Papageorgiou

Copyright © 2013 Wasim Ul-Haq and Shahid Mahmood. 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. A. W. Goodman, Univalent Functions. Vol. I, Polygonal Publishing House, Washington, DC, USA, 1983. View at Zentralblatt MATH · View at MathSciNet
  2. S. Kanas and A. Wisniowska, “Conic regions and k-uniform convexity,” Journal of Computational and Applied Mathematics, vol. 105, no. 1-2, pp. 327–336, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Kanas and A. Wisniowska, “Conic domains and starlike functions,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 45, no. 4, pp. 647–657, 2000. View at Zentralblatt MATH · View at MathSciNet
  4. M. Acu, “On a subclass of n-uniformly close to convex functions,” General Mathematics, vol. 14, no. 1, pp. 55–64, 2006. View at MathSciNet
  5. E. Aqlan, J. M. Jahangiri, and S. R. Kulkarni, “New classes of k-uniformly convex and starlike functions,” Tamkang Journal of Mathematics, vol. 35, no. 3, pp. 1–7, 2004. View at MathSciNet
  6. S. Kanas, “Alternative characterization of the class k-UCV and related classes of univalent functions,” Serdica. Mathematical Journal, vol. 25, no. 4, pp. 341–350, 1999. View at MathSciNet
  7. S. Kanas and H. M. Srivastava, “Linear operators associated with k-uniformly convex functions,” Integral Transforms and Special Functions, vol. 9, no. 2, pp. 121–132, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Shams, S. R. Kulkarni, and J. M. Jahangiri, “Classes of uniformly starlike and convex functions,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 55, pp. 2959–2961, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. M. Srivastava, S.-H. Li, and H. Tang, “Certain classes of k-uniformly close-to-convex functions and other related functions defined by using the Dziok-Srivastava operator,” Bulletin of Mathematical Analysis and Applications, vol. 1, no. 3, pp. 49–63, 2009. View at MathSciNet
  10. K. I. Noor, “On a generalization of uniformly convex and related functions,” Computers & Mathematics with Applications, vol. 61, no. 1, pp. 117–125, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. K. I. Noor and F. M. Al-Oboudi, “Alpha-quasi-convex univalent functions,” Caribbean Journal of Mathematics, vol. 3, pp. 1–8, 1984.
  12. K. I. Noor and S. N. Malik, “On generalized bounded Mocanu variation associated with conic domain,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 844–852, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. I. Noor, M. Arif, and W. Ul-Haq, “On k-uniformly close-to-convex functions of complex order,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 629–635, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  14. K. G. Subramanian, T. V. Sudharsan, and H. Silverman, “On uniformly close-to-convex functions and uniformly quasiconvex functions,” International Journal of Mathematics and Mathematical Sciences, vol. 2003, no. 48, pp. 3053–3058, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. R. J. Libera, “Some radius of convexity problems,” Duke Mathematical Journal, vol. 31, pp. 143–158, 1964. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. K. I. Noor, “On quasi-convex functions and related topics,” International Journal of Mathematics and Mathematical Sciences, vol. 2, pp. 241–258, 1987.
  17. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, vol. 225 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000. View at MathSciNet
  18. S. D. Bernardi, “Convex and starlike univalent functions,” Transactions of the American Mathematical Society, vol. 135, pp. 429–446, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. J. Libera, “Some classes of regular univalent functions,” Proceedings of the American Mathematical Society, vol. 16, pp. 755–758, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet