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Geometric properties of normalized Rabotnov function

Year 2022, Volume: 51 Issue: 5, 1248 - 1259, 01.10.2022
https://doi.org/10.15672/hujms.980307

Abstract

In the present paper, our aim is to study geometric properties of normalized Rabotnov functions. For this purpose, we determined sufficient conditions for univalency, close-to-convexity, convexity and starlikeness of the normalized Rabotnov functions in the open unit disk.

References

  • [1] D. Bansal and J.K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ. 61(3), 338350, 2016.
  • [2] D.Bansal, M.K. Soni and A. Soni, Certain geometric properties of the modified Dini function, Anal. Math. Phys. 9, 13831392, 2019.
  • [3] A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen. 73(1-2), 155178, 2008.
  • [4] PL. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, New York, NY, USA: Springer-Verlag, 1983.
  • [5] L. Fejér, Untersuchungen uber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Litt. Sci. Szeged 8, 89-115, 1936.
  • [6] A.W. Goodman, Univalent Functions, New York, NY, USA: Mariner Publishing Company, 1983.
  • [7] T.H. MacGregor, The radius of univalence of certain analytic functions II, Proc. Amer. Math. Soc. 14, 521524, 1963.
  • [8] T.H. MacGregor, A class of univalent functions, Proc. Amer. Math. Soc., 15, 311317, 1964.
  • [9] S. Ozaki, On the theory of multivalent functions, Science Reports of the Tokyo Bunrika Daigaku, Section A, 2(40), 167-188, 1935.
  • [10] S. Ponnusamy and A. Baricz, Starlikeness and convexity of generalized Bessel functions, Integral Transform Spec. Funct. 21(9), 641653, 2010.
  • [11] J.K. Prajapat, Certain geometric properties of the Wright functions, Integral Transforms Spec. Funct. 26(3), 203212, 2015.
  • [12] Y. Rabotnov, Equilibrium of an Elastic Medium with After-Effect, Prikladnaya Matematika i Mekhanika, 12, 1948, 1, pp. 53-62 (in Russian), Reprinted: Fractional Calculus and Applied Analysis, 17, 3, pp. 684-696, 2014.
  • [13] D. Raducanu, Geometric properties of Mittag-Leffler functions, Models and Theories in Social Systems, Springer: Berlin, Germany, 403-415, 2019.
  • [14] S. Sümer Eker, S. Ece, Geometric Properties of the Miller-Ross Functions Iran. J. Sci. Technol. Trans. Sci., 2022.

Year 2022, Volume: 51 Issue: 5, 1248 - 1259, 01.10.2022
https://doi.org/10.15672/hujms.980307

Abstract

References

  • [1] D. Bansal and J.K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ. 61(3), 338350, 2016.
  • [2] D.Bansal, M.K. Soni and A. Soni, Certain geometric properties of the modified Dini function, Anal. Math. Phys. 9, 13831392, 2019.
  • [3] A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen. 73(1-2), 155178, 2008.
  • [4] PL. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, New York, NY, USA: Springer-Verlag, 1983.
  • [5] L. Fejér, Untersuchungen uber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Litt. Sci. Szeged 8, 89-115, 1936.
  • [6] A.W. Goodman, Univalent Functions, New York, NY, USA: Mariner Publishing Company, 1983.
  • [7] T.H. MacGregor, The radius of univalence of certain analytic functions II, Proc. Amer. Math. Soc. 14, 521524, 1963.
  • [8] T.H. MacGregor, A class of univalent functions, Proc. Amer. Math. Soc., 15, 311317, 1964.
  • [9] S. Ozaki, On the theory of multivalent functions, Science Reports of the Tokyo Bunrika Daigaku, Section A, 2(40), 167-188, 1935.
  • [10] S. Ponnusamy and A. Baricz, Starlikeness and convexity of generalized Bessel functions, Integral Transform Spec. Funct. 21(9), 641653, 2010.
  • [11] J.K. Prajapat, Certain geometric properties of the Wright functions, Integral Transforms Spec. Funct. 26(3), 203212, 2015.
  • [12] Y. Rabotnov, Equilibrium of an Elastic Medium with After-Effect, Prikladnaya Matematika i Mekhanika, 12, 1948, 1, pp. 53-62 (in Russian), Reprinted: Fractional Calculus and Applied Analysis, 17, 3, pp. 684-696, 2014.
  • [13] D. Raducanu, Geometric properties of Mittag-Leffler functions, Models and Theories in Social Systems, Springer: Berlin, Germany, 403-415, 2019.
  • [14] S. Sümer Eker, S. Ece, Geometric Properties of the Miller-Ross Functions Iran. J. Sci. Technol. Trans. Sci., 2022.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Sevtap Sümer Eker 0000-0002-2573-0726

Sadettin Ece This is me 0000-0003-4936-3067

Publication Date October 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 5

Cite

APA Sümer Eker, S., & Ece, S. (2022). Geometric properties of normalized Rabotnov function. Hacettepe Journal of Mathematics and Statistics, 51(5), 1248-1259. https://doi.org/10.15672/hujms.980307
AMA Sümer Eker S, Ece S. Geometric properties of normalized Rabotnov function. Hacettepe Journal of Mathematics and Statistics. October 2022;51(5):1248-1259. doi:10.15672/hujms.980307
Chicago Sümer Eker, Sevtap, and Sadettin Ece. “Geometric Properties of Normalized Rabotnov Function”. Hacettepe Journal of Mathematics and Statistics 51, no. 5 (October 2022): 1248-59. https://doi.org/10.15672/hujms.980307.
EndNote Sümer Eker S, Ece S (October 1, 2022) Geometric properties of normalized Rabotnov function. Hacettepe Journal of Mathematics and Statistics 51 5 1248–1259.
IEEE S. Sümer Eker and S. Ece, “Geometric properties of normalized Rabotnov function”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, pp. 1248–1259, 2022, doi: 10.15672/hujms.980307.
ISNAD Sümer Eker, Sevtap - Ece, Sadettin. “Geometric Properties of Normalized Rabotnov Function”. Hacettepe Journal of Mathematics and Statistics 51/5 (October2022), 1248-1259. https://doi.org/10.15672/hujms.980307.
JAMA Sümer Eker S, Ece S. Geometric properties of normalized Rabotnov function. Hacettepe Journal of Mathematics and Statistics. 2022;51:1248–1259.
MLA Sümer Eker, Sevtap and Sadettin Ece. “Geometric Properties of Normalized Rabotnov Function”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, 2022, pp. 1248-59, doi:10.15672/hujms.980307.
Vancouver Sümer Eker S, Ece S. Geometric properties of normalized Rabotnov function. Hacettepe Journal of Mathematics and Statistics. 2022;51(5):1248-59.

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