Some properties of analytical functions related to Borel distribution series

Volume 26, Issue 4, pp 395--404 http://dx.doi.org/10.22436/jmcs.026.04.07

Publication Date: January 14, 2022 Submission Date: November 10, 2021 Revision Date: November 23, 2021 Accteptance Date: December 10, 2021

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Authors

H. Niranjan - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore--632014, Tamilnadu, India. A. N. Murthy - Department of Mathematics, A. V. V. Junior College, Warangal--506 002, Telangana, India. P. T. Reddy - Department of Mathematics, School of Engineering, NNRESGI, Medichal--500088, Telangana, India.

Abstract

In this paper, we introduce and study a new subclass of analytic functions which are defined by means of a linear operator. Some results connected to coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity close-to-convexity and integral means inequalities related to the subclass is obtained.

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Keywords

• Analytic
• starlike
• coefficient bounds
• convexity

MSC

•  30C45
•  30C50

References

• [1] N. Alessa, B. Venkateswarlu, P. Thirupathi Reddy, K. Loganathan, K. Tamilvanan, A New subclass of analytic functions related to Mittag-Leffler type Poisson distribution series, J. Funct. Spaces, 2021 (2021), 7 pages
  • View Article
  • MathSciNet


• [2] A. A. Attiya, Some applications of Mittag-Leffler function in the unit disk, Filomat, 30 (2016), 2075--2081
  • View Article
  • MathSciNet


• [3] D. Bansal, J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ., 61 (2016), 338--350
  • View Article
  • MathSciNet


• [4] S. M. El-Deeb, G. Murugusundaramoorthy, A. Alburaikan, Bi-Bazilevic functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials, J. Math. Computer Sci., 24 (2022), 235--245
  • View Article
  • Google Scholar


• [5] B. A. Frasin, An application of an operator associated with generalized Mittag-Leffler function, Konuralp J. Math., 7 (2019), 199--202
  • View Article
  • MathSciNet


• [6] B. A. Frasin, T. Al-Hawary, F. Yousef, Some properties of a linear operator involving generalized Mittag-Leffler function, Stud. Univ. Babes-Bolyai Math., 65 (2020), 67--75
  • View Article
  • MathSciNet


• [7] M. Grag, P. Manohar, S. L. Kalla, A Mittag-Leffler-type function of two variables, Integral Transforms Spec. Funct., 24 (2013), 934--944
  • View Article
  • MathSciNet


• [8] J. E. Littlewood, On inequalities in the theory of functions, Proc. London Math. Soc. (2), 23 (1925), 481--519
  • View Article
  • MathSciNet


• [9] G. Mittag-Leffler, Sur la Nouvelle Fonction $E_{\alpha}(x)$, Comptes Rendus de l'Academie des Sciences Paris, 137 (1903), 554--558
  • Google Scholar
  • MATH


• [10] G. Murugusundaramoorthy, S. M. El-Deeb, Second Hankel determinant for a class of analytic functions of the Mittag-Leffler-type Borel distribution related with Legendre polynomials, Turkish World Math. Soc. J. Appl. Eng. Math., accepted for publications (2021)
  • Google Scholar


• [11] S. M. Popade, R. N. Ingle, P. T. Reddy, On a certain subclass of analytic functions defined by a differential operator, Malaya J. Mat., 8 (2020), 576--580
  • View Article
  • MathSciNet


• [12] K. A. Selvakumaran, H. A. Al-Kharsani, D. Baleanu, S. D. Purohi, K. S. Nisar, Inclusion relationships for some subclasses of analytic functions associated with generalized Bessel functions, J. Comput. Anal. Appl., 24 (2018), 81--90
  • View Article
  • MathSciNet


• [13] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109--116
  • View Article
  • MathSciNet


• [14] H. Silverman, A survey with open problems on univalent functions whose coefficient are negative, Rocky Mountain J. Math., 21 (1991), 1099--1125
  • View Article
  • MathSciNet


• [15] H. Silvermani, Integral means for univalent functions with negative coefficient, Houston J. Math., 23 (1997), 169--174
  • View Article
  • MathSciNet


• [16] H. M. Srivastava, G. Murugusundaramoorthy, S. M. El-Deeb, Faber polynomial coefficient estimates of bi-close-to-convex functions connected with the Borel distribution of the Mittag-leffler type, J. Nonlinear Var. Anal., 5 (2021), 103--118
  • View Article
  • Google Scholar


• [17] A. K. Wanas, J. A. Khuttar, Applications of Borel distribution series on analytic functions, Earthline J. Math. Sci., 4 (2020), 71--82
  • View Article
  • Google Scholar


• [18] A. Wiman, Über die Nullstellen der Funktionen $E_a(x)$, Acta Math., 29 (1905), 217--234
  • View Article
  • MathSciNet