Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON SOME DIFFERENTIAL SUBORDINATION INVOLVING THE BESSEL-STRUVE KERNEL FUNCTION

  • Al-Dhuain, Mohammed (Department of Mathematics King Faisal University) ;
  • Mondal, Saiful R. (Department of Mathematics King Faisal University)
  • Received : 2017.04.03
  • Accepted : 2017.06.19
  • Published : 2018.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. Some open problems with this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.

Keywords

References

  1. R. M. Ali, R. Chandrashekar, and V. Ravichandran, Janowski starlikeness for a class of analytic functions, Appl. Math. Lett. 24 (2011), no. 4, 501-505. https://doi.org/10.1016/j.aml.2010.11.001
  2. R. M. Ali, S. Nagpal, and V. Ravichandran, Second-order differential subordination for analytic functions with fixed initial coeffcient, Bull. Malays. Math. Sci. Soc. (2) 34 (2011), no. 3, 611-629.
  3. R. M. Ali, V. Ravichandran, and N. Seenivasagan, Suffcient conditions for Janowski starlikeness, Int. J. Math. Math. Sci. 2007 (2007), Art. ID 62925, 7 pp.
  4. R. M. Ali, Subordination and superordination on Schwarzian derivatives, J. Inequal. Appl. 2008 (2008), Art. ID 712328, 18 pp.
  5. R. M. Ali, Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc. (2) 31 (2008), no. 2, 193-207.
  6. R. M. Ali, Differential subordination and superordination of analytic functions defined by the multiplier transformation, Math. Inequal. Appl. 12 (2009), no. 1, 123-139.
  7. R. M. Ali, Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava linear operator, J. Franklin Inst. 347 (2010), no. 9, 1762-1781. https://doi.org/10.1016/j.jfranklin.2010.08.009
  8. R. M. Ali, On subordination and superordination of the multiplier transformation formeromorphic functions, Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 2, 311-324.
  9. J. A. Antonino and S. S. Miller, Third-order differential inequalities and subordinationsin the complex plane, Complex Var. Elliptic Equ. 56 (2011), no. 5, 439-454. https://doi.org/10.1080/17476931003728404
  10. A. Gasmi and M. Sifi, The Bessel-Struve intertwining operator on C and mean-periodic functions, Int. J. Math. Math. Sci. 2004 (2004), no. 57-60, 3171-3185. https://doi.org/10.1155/S0161171204309178
  11. A. Gasmi and F. Soltani, Fock spaces for the Bessel-Struve kernel, J. Anal. Appl. 3 (2005), no. 2, 91-106.
  12. A. W. Goodman, Univalent functions. Vol. I & II, Mariner, Tampa, FL, 1983.
  13. S. Hamem, L. Kamoun, and S. Negzaoui, Cowling-Price type theorem related to Bessel-Struve transform, Arab J. Math. Sci. 19 (2013), no. 2, 187-198. https://doi.org/10.1016/j.ajmsc.2012.09.003
  14. W. Janowski, Some extremal problems for certain families of analytic functions. I, Ann. Polon. Math. 28 (1973), 297-326. https://doi.org/10.4064/ap-28-3-297-326
  15. S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), no. 2, 199-211. https://doi.org/10.1016/0022-0396(87)90146-X
  16. S. S. Miller, Differential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Dekker, New York, 2000.
  17. H. Tang and E. Deniz, Third-order Differential subordination results for analytic functions involving the generalized Bessel functions, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 6, 1707-1719.