COEFFICIENT INEQUALITIES OF A GENERALISED DISTRIBUTION ASSOCIATED WITH A GENERALIZED KOEBE FUNCTION
##plugins.themes.EpsilonTheme.article.main##
Olushola Adeyemo*
Sayo Abidemi Gbabgbala
This study aims to explore the geometric properties of the generalized probability distribution associated with the generalized Koebe function. The inequality coefficients in the convoluted power series are evaluated using Chebyshev polynomials, with a focus on determining bounds on the initial coefficients. This research employs a mathematical-theoretic approach utilizing algebraic manipulations, theorem proving, and analytical techniques such as subordination and Hadamard products. Few conditions were set on some variables which yields certain corollaries. The results suggest that the analyzed functions have properties that are applicable in modeling complex data, allowing the description of non-normal, asymmetric, or heavy-tailed probability distributions. These findings corroborate the relevance of generalized distributions in dealing with uncertainty and variability in statistical data. Based on the existing works, the results obtained in this work are just derived. In conclusion, this study contributes to understanding the geometric relationships of generalized probability distributions. The practical implications of these findings include applications in the analysis of complex statistical data and modeling of real-world phenomena that require non-conventional distributions.
Adeyemo, O., Oladipo, A, T., and El-Ashwah, R. M. (2023). Truncated Tangent; polynomial equipped with generalized Pascal Snail. Annals of Oradea University-Mathematics Fascicola, 30(1), 119–128.
Al-Ziadi, N. A. J., and Ramadhan, A. M. (2022). A New Class of Holomorphic Univalent Functions Defined by Linear Operator. Journal of Advances in Mathematics, 21, 116–124.
Altintas, O., and Owa, S. (1988). On subclasses of univalent functions with negative coefficients. East Asian Mathematical Journal, 4, 41–56.
Darus, M., and Owa, S. (2017). New subclasses concerning some analytic and univalent functions. Chinese Journal of Mathematics, 2017(1), 4674782.
Doha, E. H. (1994). The first and second kind chebyshev coefficients of the moments for the general order derivative on an infinitely differentiable function. International Journal of Computer Mathematics, 51(1–2), 21–35.
Hassan, L. H., and Al-Ziadi, N. A. J. (2023). New Class of p-valent Functions Defined by Multiplier Transformations. Utilitas Mathematica, 120, 182–200.
Liu, D., Araci, S., and Khan, B. (2021). A subclass of Janowski starlike functions involving Mathieu-type series. Symmetry, 14(1), 2.
Mason, J. C. (1967). Chebyshev polynomial approximations for the L-membrane eigenvalue problem. SIAM Journal on Applied Mathematics, 15(1), 172–186.
Mostafa, A. O. (2009). A study on starlike and convex properties for hypergeometric functions. J. Inequal. Pure Appl. Math, 10(3), 1–16.
Oladipo, A. T. (2016). Coefficient inequality for subclass of analytic univalent functions related to simple logistic activation functions. Stud. Univ. Babes-Bolyai Math, 61(1), 45–52.
Oladipo, A. T. (2019). Generalized distribution associated with univalent functions in a conical domain. Analele Universitatii Oradea, Fasc. M Atematica,Tom XXVI, 1, 163–169.
Oladipo, A. T. (2020). Bounds for probabilities of the generalized distribution defined by generalized polylogarithm. Punjab University Journal of Mathematics, 51(7).
Oladipo, A. T., and Opoola, T. O. (2010). On Coefficient Bounds of A Subclass of Univalent Functions. Journal of the Nigerian Association of Mathematical Physics, 16, 395–400.
Porwal, S. (2013). Mapping properties of generalized Bessel functions on some subclasses of univalent functions. Anal. Univ. Oradea Fasc. Matematica, 20(2), 51–60.
Porwal, S. (2014). An application of a Poisson distribution series on certain analytic functions. Journal of Complex Analysis, 2014(1), 984135.
Porwal, S. (2018). Generalized distribution and its geometric properties associated with univalent functions. Journal of Complex Analysis, 2018(1), 8654506.
Rossdy, M., Omar, R., and Soh, S. C. (2024). New differential operator for analytic univalent functions associated with binomial series. AIP Conference Proceedings, 2905(1).
Sharma, A. K., Porwal, S., and Dixit, K. K. (2013). Class mappings properties of convolutions involving certain univalent functions associated with hypergeometric functions. Electronic J. Math. Anal. Appl, 1(2), 326–333.
Silverman, H. (1975). Univalent functions with negative coefficients. Proceedings of the American Mathematical Society, 51(1), 109–116.
Wanas, A. K., and Ahsoni, H. M. (2022). Some geometric properties for a class of analytic functions defined by beta negative binomial distribution series. Earthline Journal of Mathematical Sciences, 9(1), 105–116.
Whittaker, E. T., and Watson, G. N. (1963). A course of modern analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions (4th ed). Cambridge university proceeding.
