DOI QR코드

DOI QR Code

ON PARTIAL SUMS OF NORMALIZED q-BESSEL FUNCTIONS

  • Aktas, Ibrahim (Department of Mathematical Engineering Gumushane University) ;
  • Orhan, Halit (Department of Mathematics Ataturk University)
  • 투고 : 2017.05.15
  • 심사 : 2017.11.02
  • 발행 : 2018.04.30

초록

In the present investigation our main aim is to give lower bounds for the ratio of some normalized q-Bessel functions and their sequences of partial sums. Especially, we consider Jackson's second and third q-Bessel functions and we apply one normalization for each of them.

키워드

참고문헌

  1. I. Aktas and A. Baricz, Bounds for radii of starlikeness of some q-Bessel functions, Results Math. 72 (2017), no. 1-2, 947-963. https://doi.org/10.1007/s00025-017-0668-6
  2. I. Aktas and H. Orhan, Distortion bounds for a new subclass of analytic functions and their partial sums, Bull. Transilv. Univ. Brasov Ser. III 8(57) (2015), no. 2, 1-11 pp.
  3. I. Aktas, Partial sums of normalized Dini functions, J. Class. Anal. 9 (2016), no. 2, 127-135.
  4. M. H. Annaby and Z. S. Mansour, q-fractional calculus and equations, Lecture Notes in Mathematics, 2056, Springer, Heidelberg, 2012.
  5. A. Baricz, D. K. Dimitrov, and I. Mezo Radii of starlikeness and convexity of some q-Bessel functions, J. Math. Anal. Appl. 435 (2016), no. 1, 968-985. https://doi.org/10.1016/j.jmaa.2015.10.065
  6. A. Baricz, D. K. Dimitrov, H. Orhan, and N. Yagmur, Radii of starlikeness of some special functions, Proc. Amer. Math. Soc. 144 (2016), no. 8, 3355-3367. https://doi.org/10.1090/proc/13120
  7. M. Caglar and E. Deniz, Partial sums of the normalized Lommel functions, Math. Inequal. Appl. 18 (2015), no. 3, 1189-1199.
  8. H. Orhan and N. Yagmur, Partial sums of generalized Bessel functions, J. Math. Inequal. 8 (2014), no. 4, 863-877.
  9. S. Owa, H. M. Srivastava, and N. Saito, Partial sums of certain classes of analytic functions, Int. J. Comput. Math. 81 (2004), no. 10, 1239-1256. https://doi.org/10.1080/00207160412331284042
  10. D. Raducanu, On partial sums of normalized Mittag-Leffer functions, An. St. Univ. Ovidius Constanta, 25 (2017), no. 2, 123-133.
  11. T. Sheil-Small, A note on the partial sums of convex schlicht functions, Bull. Lond. Math. Soc. 2 (1970), 165-168. https://doi.org/10.1112/blms/2.2.165
  12. H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), no. 1, 221-227. https://doi.org/10.1006/jmaa.1997.5361
  13. E. M. Silvia, On partial sums of convex functions of order ${\alpha}$, Houston J. Math. 11 (1985), no. 3, 397-404.