Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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STARLIKENESS OF q-DIFFERENTIAL OPERATOR INVOLVING QUANTUM CALCULUS

  • Aldawish, Ibtisam (School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia) ;
  • Darus, Maslina (School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia)
  • Received : 2014.09.27
  • Accepted : 2014.12.11
  • Published : 2014.12.30
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Abstract

In the present paper, we investigate starlikeness conditions for q-differential operator by using the concept of quantum calculus in the unit disk.

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References

  1. F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math and Math Sci 25-28 (2004), 1429-1436.
  2. H. Aldweby and M. Darus, Some subordination results on q-Analogue of Ruscheweyh differential operator, Abstr. Appl. Anal. (2014) Article ID958563, 6 pages.
  3. I. Aldawish and M. Darus, New subclass of analytic function associated with the generlalized hypergeometric functions, Electronic J. Math. Anal. Appl. 2 (2) (2014), 163-171.
  4. A. Aral, V. Gupta Ravi and P. Agarwal, Applications of q Calculus in operator Theory, New york, NY: Springer, 2013.
  5. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (4) (1984), 737-745. https://doi.org/10.1137/0515057
  6. J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13. https://doi.org/10.1016/S0377-0427(98)00235-0
  7. H. Exton, q-hypergeometric Functions and Applications, Ellis Horwood Limited, Chichester, 1983.
  8. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Math-ematics and its Application, Vol. 35, Cambridge University Press, Cambridge, 1990.
  9. H. A. Ghany, q-derivative of basic hypergeometric series with respect to parameters, Int. J. Math. Anal. (Ruse) 3 (33-36) (2009), 1617-1632.
  10. F. H. Jackson, On q-functions and a certain difference operator. Tranc. Roy. Soc. Edin 46 (1908), 253-281.
  11. K. Kuroki and S. Owa, Double integral operators concerning starlike of order $\beta$, Int. J. Differ. Equ. (2009), 1-13.
  12. S. S. Miller and P. T. Mocanu, Double integral starlike operators, Integral Trans-forms Spec. Funct. 19 (7-8) (2008), 591-597 . https://doi.org/10.1080/10652460802045282
  13. A. Mohammed and M. Darus, A generalized operator involving the q-hypergeometric function, Mat. Vesnik, 65 (4) (2013), 454-465.
  14. M. Obradovic, Simple suficient conditions for univalence, Mat. Vesnik, 49 (3-4) (1997), 241-244.
  15. D. Purohit and R. K. Raina, Generalized q-Taylor's series and applications, Gen. Math. 18 (3) (2010), 19-28.
  16. S. Rusheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.
  17. G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math. (Springer Verlag), 1013 (1983), 362-372.
  18. W.S. Chung, T. Kim, H. I. Kwon, On the q-analog of the Laplace transform, Russ. J. Math. Phys. 21 (2) (2014), 156-168. https://doi.org/10.1134/S1061920814020034
  19. J. Yang, U(n+1) extensions of some basic hypergeometric series identities. Adv. Stud. Contemp. Math. (Kyungshang) 18 (2) (2009), 201-218.
  20. Y. S. Kim, C. H. Lee, Exton's triple hypergeometric series associated with the Kamp De Friet function, Proc. Jangjeon Math. Soc. 14 (4) (2011), 447-453.
  21. K. R. Vasuki, A. A. Kahtan, G. Sharath, On certain continued fractions related to $_3{\psi}_3$ basic bilateral hypergeometric functions, Adv. Stud. Contemp. Math. (Kyungshang) 20 (3) (2010) 343-357.

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