Research Article
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Year 2020, Volume: 49 Issue: 1, 380 - 388, 06.02.2020
https://doi.org/10.15672/hujms.470930

Abstract

References

  • [1] İ. Aktaş and H. Orhan, Distortion bounds for a new subclass of analytic functions and their partial sums, Bull. Transilv. Univ. Braşov Ser. III, 57 (2), 1–12, 2015.
  • [2] İ. Aktaş and H. Orhan, Partial sums of Normalized Dini Functions, J. Classical Anal. 9 (2), 127–135, 2016.
  • [3] İ. Aktaş and H. Orhan, On Partial sums of Normalized q-Bessel Functions, Commun. Korean Math. Soc. 33 (2), 535–547, 2018.
  • [4] D. Bansal and H. Orhan, Partial sums of Mittag-Leffler function, J. Math. Inequal. 12 (2), 423–431, 2018.
  • [5] H. Chaggara and N.B. Romdhane, On the zeros of the hyper-Bessel function, Integral Transforms Spec. Funct. 26 (2), 96–101, 2015.
  • [6] M. Çağlar and E. Deniz, Partial sums of the normalized Lommel functions, Math. Inequal. Appl. 18 (3), 1189–1199, 2015.
  • [7] B.A. Frasin, Generalization of partial sums of certain analytic and univalent functions, Appl. Math. Lett. 21, 735-741, 2008.
  • [8] A.W. Goodman, Univalent functions, vol. 1, Mariner Publishing Company, Inc., 1983.
  • [9] H. Orhan and N. Yağmur, Partial sums of Generilazed Bessel Functions, J. Math. Inequal. 8 (4), 863–877, 2014.
  • [10] S. Owa, H.M. Srivastava and N. Saito, Partial sums of certain classes of analytic functions, Int. J. Comput. Math. 81 (10), 1239–1256, 2004.
  • [11] D. Răducanu, On partial sums of normalized Mittag-Leffler functions, An. Şt. Univ. Ovidius Constanta, 25 (2), 123–133, 2017.
  • [12] T. Sheil-Small, A note on partial sums of convex schlicht functions, Bull. London Math. Soc. 2, 165–168, 1970.
  • [13] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209, 221–227, 1997.
  • [14] E.M. Silvia, On partial sums of convex functions of order α. Houston J. Math. 11, 397–404, 1985.
  • [15] G.N. Watson, A Tretaise on the Theory of Bessel Functions. Second edition, London and New York, Cambridge University Press, 1944.
  • [16] N. Yağmur and H. Orhan, Partial sums of Generilazed Struve Functions, Miskolc Math. Notes, 17 (1), 657-670, 2016.

Partial sums of hyper-Bessel function with applications

Year 2020, Volume: 49 Issue: 1, 380 - 388, 06.02.2020
https://doi.org/10.15672/hujms.470930

Abstract

The main purpose of the presented paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its partial sum. In addition, some applications related to the obtained results are given.

References

  • [1] İ. Aktaş and H. Orhan, Distortion bounds for a new subclass of analytic functions and their partial sums, Bull. Transilv. Univ. Braşov Ser. III, 57 (2), 1–12, 2015.
  • [2] İ. Aktaş and H. Orhan, Partial sums of Normalized Dini Functions, J. Classical Anal. 9 (2), 127–135, 2016.
  • [3] İ. Aktaş and H. Orhan, On Partial sums of Normalized q-Bessel Functions, Commun. Korean Math. Soc. 33 (2), 535–547, 2018.
  • [4] D. Bansal and H. Orhan, Partial sums of Mittag-Leffler function, J. Math. Inequal. 12 (2), 423–431, 2018.
  • [5] H. Chaggara and N.B. Romdhane, On the zeros of the hyper-Bessel function, Integral Transforms Spec. Funct. 26 (2), 96–101, 2015.
  • [6] M. Çağlar and E. Deniz, Partial sums of the normalized Lommel functions, Math. Inequal. Appl. 18 (3), 1189–1199, 2015.
  • [7] B.A. Frasin, Generalization of partial sums of certain analytic and univalent functions, Appl. Math. Lett. 21, 735-741, 2008.
  • [8] A.W. Goodman, Univalent functions, vol. 1, Mariner Publishing Company, Inc., 1983.
  • [9] H. Orhan and N. Yağmur, Partial sums of Generilazed Bessel Functions, J. Math. Inequal. 8 (4), 863–877, 2014.
  • [10] S. Owa, H.M. Srivastava and N. Saito, Partial sums of certain classes of analytic functions, Int. J. Comput. Math. 81 (10), 1239–1256, 2004.
  • [11] D. Răducanu, On partial sums of normalized Mittag-Leffler functions, An. Şt. Univ. Ovidius Constanta, 25 (2), 123–133, 2017.
  • [12] T. Sheil-Small, A note on partial sums of convex schlicht functions, Bull. London Math. Soc. 2, 165–168, 1970.
  • [13] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209, 221–227, 1997.
  • [14] E.M. Silvia, On partial sums of convex functions of order α. Houston J. Math. 11, 397–404, 1985.
  • [15] G.N. Watson, A Tretaise on the Theory of Bessel Functions. Second edition, London and New York, Cambridge University Press, 1944.
  • [16] N. Yağmur and H. Orhan, Partial sums of Generilazed Struve Functions, Miskolc Math. Notes, 17 (1), 657-670, 2016.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

İbrahim Aktaş 0000-0003-4570-4485

Publication Date February 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 1

Cite

APA Aktaş, İ. (2020). Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics, 49(1), 380-388. https://doi.org/10.15672/hujms.470930
AMA Aktaş İ. Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics. February 2020;49(1):380-388. doi:10.15672/hujms.470930
Chicago Aktaş, İbrahim. “Partial Sums of Hyper-Bessel Function With Applications”. Hacettepe Journal of Mathematics and Statistics 49, no. 1 (February 2020): 380-88. https://doi.org/10.15672/hujms.470930.
EndNote Aktaş İ (February 1, 2020) Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics 49 1 380–388.
IEEE İ. Aktaş, “Partial sums of hyper-Bessel function with applications”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, pp. 380–388, 2020, doi: 10.15672/hujms.470930.
ISNAD Aktaş, İbrahim. “Partial Sums of Hyper-Bessel Function With Applications”. Hacettepe Journal of Mathematics and Statistics 49/1 (February 2020), 380-388. https://doi.org/10.15672/hujms.470930.
JAMA Aktaş İ. Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics. 2020;49:380–388.
MLA Aktaş, İbrahim. “Partial Sums of Hyper-Bessel Function With Applications”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, 2020, pp. 380-8, doi:10.15672/hujms.470930.
Vancouver Aktaş İ. Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):380-8.