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Geometric properties of normalized Rabotnov function

Year 2022, , 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, , 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 Mathematics
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

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 (October 2022), 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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