A new subclass of analytic functions involving Pascal distribution series

Document Type : Research Paper

Authors

1 Department of Mathematics, GSS, GITAM University, Doddaballapur-562 163, Bengaluru Rural, Karnataka, India

2 Department of Mathematics, Kakatiya Univeristy, Warangal-506 009, Telangana, India

Abstract

In this work, we introduce and investigate a new class $ k- \widetilde{ U}ST_s (q , m , \gamma, \varsigma )$ of analytic functions in the open unit disc $U$ with negative coefficients. The aim of this study is to determine coefficient estimates, neighborhoods and partial sums for functions $u$ belonging to this class.

Keywords

[1] E. Aqlan, J.M. Jhangiri and S.R. Kulkarni, Classes of k−uniformly convex and starlike functions, Tamkang J. Math. 35 (2004) 1–7.
[2] N.E. Cho, S.Y. Woo and S. Owa, Uniform convexity properties for hypergeometric functions, Fract. Calc. Appl. Anal. 5(3) (2002) 303–313.
[3] L. De Branges, A proof of the Bieberbach conjecture, Acta Math. 154(1-2) (1985) 137–152.
[4] S.M. El-Deeb, T. Bulboaca and J. Dziok, Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Math. J. 59 (2) (2019) 301–314.
[5] A.W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598–601.
[6] A.W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991) 364–370.
[7] E.P. Merkes and W.T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc. 12 (1961) 885–888.
[8] A.O. Mostafa, A study on starlike and convex properties for hypergeometric functions, J. Inequal. Pure Appl. Math. 10(3) (2009) Article 87, 8 pp.
[9] G. Murugusundaramoorthy, Subclasses of starlike and convex functions involving Poisson distribution series, Afr. Mat. 28(7-8) (2017) 1357–1366.
[10] G. Murugusundaramoorthy, K. Vijaya and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacet. J. Math. Stat. 45(4) (2016) 1101–1107.
[11] S. Owa, T. Sekine and R. Yamakawa, On Sakaguchi type functions, Appl. Math. Comput. 187 (2007) 356–361.
[12] F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993) 189–196.
[13] S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81 (4), 521–527, 1981.
[14] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan, 11 (1959), 72–75.
[15] H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl. 172(2) (1993) 574–581.
[16] H. Silverman, Partial sums of starlike and convex functions, J. Anal. Appl. 209 (1997) 221–227.
[17] E.M. Silvia, Partial sums of convex functions of order R, Houston J. Math. 11(3) (1985) 397–404.
[18] H.M. Srivastava, G. Murugusundaramoorthy and S. Sivasubramanian, Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integral Transforms Spec. Funct. 18(7-8) (2007) 511–520.
[19] P. Thirupathi Reddy and B. Venkateswarlu, New subclass of analytic functions involving Hurwitz Lerch zeta functions, Int. J. Math. Comput. 31(1) (2020) 76–83
Volume 13, Issue 1
March 2022
Pages 3141-3152
  • Receive Date: 15 August 2020
  • Accept Date: 12 April 2021