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Year 2020, Volume: 5 Issue: 1, 16 - 22, 30.03.2020

Abstract

References

  • \.{I}. Akta\c{s}, \'A. Baricz, Bounds for radii of starlikeness of some $q-$Bessel functions, Results Math (2017), \textbf{72}(71): 947--963.
  • \.{I}. Akta\c{s}, \'A. Baricz, S. Singh, Geometric and monotonic properties of hyper-Bessel functions, {\it Ramanujan J.} (2019), 1--21, doi: 10.1007/s11139-018-0105-9
  • R.M. Ali, N. K. Jain, V. Ravichandran, Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, {\it Appl. Math. Comput.} (2012), \textbf{218}, no. 11, 6557–6565.
  • \'A. Baricz, A. Prajapati, Radii of starlikeness and convexity of generalized Mittag-Leffler functions, arXiv preprint \href{https://arxiv.org/abs/1901.04333}{arXiv:1901.04333} (2019)
  • \'A. Baricz, E. Toklu, E. Kad{\i}o\u{g}lu, Radii of starlikeness and convexity of Wright functions, {\it Math. Commun.} (2018), 23: 97--117.
  • H. Chaggara, N.B. Romdhane, On the zeros of the hyper-Bessel function, {\it Integr. Transf. Spec. Funct.} (2015), \textbf{26}(2), 96--101.
  • A. W. Goodman, {\it Univalent functions. Vol. I}, Mariner Publishing Co., Inc., Tampa, FL, 1983.
  • W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, {\it Ann. Polon. Math.}, \textbf{23} (1970/1971), 159–177.
  • V. Madaan, A. Kumar, V. Ravichandran, Lemniscate Convexity and Other Properties of Generalized Bessel Functions. arXiv preprint \href{https://arxiv.org/abs/1902.04277}{arXiv:1902.04277} (2019).
  • V. Madaan, A. Kumar, V. Ravichandran, Radii of starlikeness and convexity of Bessel functions. arXiv preprint \href{https://arxiv.org/abs/1906.05547}{arXiv:1906.05547} (2019).
  • J. Sok\'ol, J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, {\it Zeszyty Nauk. Politech. Rzeszowskiej Mat.} (1996), No. \textbf{19}, 101–105.
  • E. Toklu, \.{I}. Akta\c{s}, H. Orhan, Radii problems for normalized $q-$Bessel and Wright functions. {\it Acta Univ Sapientiae Mathematica} (2019), \textbf{11}(1): 203--223.
  • S. Verma, V. Ravichandran, Radius problems for ratios of Janowski starlike functions with their derivatives, {\it Bull. Malays. Math. Sci. Soc.} (2017) \textbf{40}, no. 2, 819–840.

Radii Problems for Normalized Hyper-Bessel Function

Year 2020, Volume: 5 Issue: 1, 16 - 22, 30.03.2020

Abstract

The main purpose of the present paper is to ascertain the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B

References

  • \.{I}. Akta\c{s}, \'A. Baricz, Bounds for radii of starlikeness of some $q-$Bessel functions, Results Math (2017), \textbf{72}(71): 947--963.
  • \.{I}. Akta\c{s}, \'A. Baricz, S. Singh, Geometric and monotonic properties of hyper-Bessel functions, {\it Ramanujan J.} (2019), 1--21, doi: 10.1007/s11139-018-0105-9
  • R.M. Ali, N. K. Jain, V. Ravichandran, Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, {\it Appl. Math. Comput.} (2012), \textbf{218}, no. 11, 6557–6565.
  • \'A. Baricz, A. Prajapati, Radii of starlikeness and convexity of generalized Mittag-Leffler functions, arXiv preprint \href{https://arxiv.org/abs/1901.04333}{arXiv:1901.04333} (2019)
  • \'A. Baricz, E. Toklu, E. Kad{\i}o\u{g}lu, Radii of starlikeness and convexity of Wright functions, {\it Math. Commun.} (2018), 23: 97--117.
  • H. Chaggara, N.B. Romdhane, On the zeros of the hyper-Bessel function, {\it Integr. Transf. Spec. Funct.} (2015), \textbf{26}(2), 96--101.
  • A. W. Goodman, {\it Univalent functions. Vol. I}, Mariner Publishing Co., Inc., Tampa, FL, 1983.
  • W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, {\it Ann. Polon. Math.}, \textbf{23} (1970/1971), 159–177.
  • V. Madaan, A. Kumar, V. Ravichandran, Lemniscate Convexity and Other Properties of Generalized Bessel Functions. arXiv preprint \href{https://arxiv.org/abs/1902.04277}{arXiv:1902.04277} (2019).
  • V. Madaan, A. Kumar, V. Ravichandran, Radii of starlikeness and convexity of Bessel functions. arXiv preprint \href{https://arxiv.org/abs/1906.05547}{arXiv:1906.05547} (2019).
  • J. Sok\'ol, J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, {\it Zeszyty Nauk. Politech. Rzeszowskiej Mat.} (1996), No. \textbf{19}, 101–105.
  • E. Toklu, \.{I}. Akta\c{s}, H. Orhan, Radii problems for normalized $q-$Bessel and Wright functions. {\it Acta Univ Sapientiae Mathematica} (2019), \textbf{11}(1): 203--223.
  • S. Verma, V. Ravichandran, Radius problems for ratios of Janowski starlike functions with their derivatives, {\it Bull. Malays. Math. Sci. Soc.} (2017) \textbf{40}, no. 2, 819–840.
There are 13 citations in total.

Details

Primary Language English
Journal Section Volume V, Issue I, 2020
Authors

Evrim Toklu 0000-0002-2332-0336

Osman Kara 0000-0003-0650-4253

Publication Date March 30, 2020
Published in Issue Year 2020 Volume: 5 Issue: 1

Cite

APA Toklu, E., & Kara, O. (2020). Radii Problems for Normalized Hyper-Bessel Function. Turkish Journal of Science, 5(1), 16-22.
AMA Toklu E, Kara O. Radii Problems for Normalized Hyper-Bessel Function. TJOS. March 2020;5(1):16-22.
Chicago Toklu, Evrim, and Osman Kara. “Radii Problems for Normalized Hyper-Bessel Function”. Turkish Journal of Science 5, no. 1 (March 2020): 16-22.
EndNote Toklu E, Kara O (March 1, 2020) Radii Problems for Normalized Hyper-Bessel Function. Turkish Journal of Science 5 1 16–22.
IEEE E. Toklu and O. Kara, “Radii Problems for Normalized Hyper-Bessel Function”, TJOS, vol. 5, no. 1, pp. 16–22, 2020.
ISNAD Toklu, Evrim - Kara, Osman. “Radii Problems for Normalized Hyper-Bessel Function”. Turkish Journal of Science 5/1 (March 2020), 16-22.
JAMA Toklu E, Kara O. Radii Problems for Normalized Hyper-Bessel Function. TJOS. 2020;5:16–22.
MLA Toklu, Evrim and Osman Kara. “Radii Problems for Normalized Hyper-Bessel Function”. Turkish Journal of Science, vol. 5, no. 1, 2020, pp. 16-22.
Vancouver Toklu E, Kara O. Radii Problems for Normalized Hyper-Bessel Function. TJOS. 2020;5(1):16-22.