International Journal of Nonlinear Analysis and Applications

On coefficients of a new Ma-Minda type class connected to binomial distribution

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In this paper, we define a new Ma-Minda type class based on binomial distribution series. Our investigation will be focused on the coefficientsof the function f belonging to that class.

Keywords

[1] R.M. Ali, S.K. Lee, V. Ravichandran, and S. Supramaniam, The Fekete-Szego coefficient functional for the transforms of analytic functions, Bull. Iran. Math. Soc. 35 (2009), no. 2, 119–142.
[2] R.M. Ali, V. Ravichandran, and N. Seenivasagan, Coefficient bounds for p-valent functions, Appl. Math. Comput. 187 (2006), no. 1, 35–46.
[3] P.L. Duren, Univalent Functions, Springer-Verlag, New York Inc, 1983.
[4] N.E. Cho, V. Kumar, S.S. Kumar, and V. Ravichandran, Radius problems for starlike functions associated with the Sine function, Bull. Iran. Math. Soc. 45 (2019), 213–232.
[5] W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, Ann. Polonici Math. 23 (1970), 159–177.
[6] R. Kargar and L. Trojnar-Spelina, Starlike functions associated with the generalized Koebe function, Anal. Math. Phys. 11 (2021), 1-26.
[7] R. Kargar, A. Ebadian, and L. Trojnar-Spelina, Further results for starlike functions related with Booth lemniscate, Iran. J. Sci. Technol. Trans. A 43 (2019), 1235–1238.
[8] V. Kumar, N.E. Cho, V. Ravichandran, and H.M. Srivastava, Sharp coefficient bounds for starlike functions associated with the Bell numbers, Math. Slovaca 69 (2019), 1053–1064.
[9] S. Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2016), 199–212.
[10] W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, Proc. Conf. Complex Anal., Tianjin-China, International Press Inc, 1992, pp. 157–169.
[11] R. Mendiratta, S. Nagpal, and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc. 38 (2015), 365–386.
[12] Z. Nehari, Conformal Mapping, McGraw-Hill, New York, NY, USA, 1952.
[13] C. Pommerenke, On the Hankel determinants of univalent functions, Mathematika 14 (1967), no. 1, 108–112.
[14] S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal. 2014 (2014), 1–3.
[15] D.V. Prokhorov and J. Szynal, Inverse coefficients for (α, β)-convex functions, Ann. Univer. Mariae Curie-Sklodowska, sectio A 35 (1981), no. 1984, 125–143.
[16] R.K. Raina, and J. Soko l, Some properties related to a certain class of starlike functions, Compt. Rendus Math. 353 (2015), no. 11, 973–978.
[17] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc. 48 (1943), no. 1, 48–82.
[18] K. Sharma, N.K. Jain, and V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat. 27 (2016), 923–939.
[19] J. Soko l, A certain class of starlike functions, Comput. Math. Appl. 62 (2011), no. 2, 611–619.
[20] J. Soko l and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Naukowe 19 (1996), 101–105.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 7
July 2024
Pages 349-358
  • Receive Date: 22 April 2023
  • Revise Date: 17 July 2023
  • Accept Date: 20 July 2023