Geometric properties of normalized Rabotnov function

Year 2022, Volume: 51 Issue: 5, 1248 - 1259, 01.10.2022

Sevtap Sümer Eker , Sadettin Ece

https://doi.org/10.15672/hujms.980307

Cited By: 10

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.

Keywords

close to convex, Rabotnov function, univalent, starlike, convex and close-to-convex

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.