Analytic Property of a Generalized Poisson Distribution

  • O.E. Opaleye Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso P.M.B. 4000, Ogbomoso, Oyo State, Nigeria
  • S.O. Fawale Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso P.M.B. 4000, Ogbomoso, Oyo State, Nigeria
  • P.O. Awoleye Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso P.M.B. 4000, Ogbomoso, Oyo State, Nigeria
  • S. Sunday Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso P.M.B. 4000, Ogbomoso, Oyo State, Nigeria
DOI: https://doi.org/10.34198/ejms.9222.265277
Keywords: Toeplitz determinant, analytic functions, coefficient bounds, Poisson distribution series, Fekete-Szegö inequalities

Abstract

Basic properties of probability with Poisson distribution is used in obtaining the coefficient bound by subordination principle which is the fundamental purpose of this work. A class of analytic function $f:\xi \rightarrow \mathbb{C}$ with unit disc $\xi :\{z\in\mathbb{C}:|z|<1\}$ is established. Likewise known results of Fekete-Szegö inequalities type and the second bound of Toeplitz determinant are obtained.

References

Abiodun Tinuoye Oladipo, Generalized distribution associated with univalent functions in conical domain, An. Univ. Oradea Fasc. Mat. 26(1) (2019), 161-167.

Abiodun Tinuoye Oladipo, Bounds for probabilities of the generalized distribution defined by generalized polylogarithm, Punjab University Journal of Mathematics 51(7) (2019), 19-26.

D. K. Thomas and S. A. Halim, Toeplitz matrices whose elements are the coefficient of starlike and close-to-convex functions, Bull. Malays. Math. Sci. Soc. 40(4) (2017), 1781-1790.

Ş. Altinkaya and S. Yalçin, Poisson distribution series for analytic univalent functions, Complex Anal. Oper. Theory 12 (2018), 1315-1319. https://doi.org/10.1007/s11785-018-0764-y

Ş. Altinkaya and S. Yalçin, Poisson distribution series for certain subclasses of starlike functions with negative coefficients, An. Univ. Oradea Fasc. Mat. 24(2) (2017), 5-8.

O. E. Opaleye, S. O. Fawale, P. O. Awoleye and P. O. Oyewo, Some geometry properties of a class of analytic function with Gegenbauer polynomial, Global Scientific Journals 10(3) (2022), 94-100.

Published
2022-05-12
How to Cite
Opaleye, O., Fawale, S., Awoleye, P., & Sunday, S. (2022). Analytic Property of a Generalized Poisson Distribution. Earthline Journal of Mathematical Sciences, 9(2), 265-277. https://doi.org/10.34198/ejms.9222.265277
Issue
Vol 9 No 2 (2022)
Section
Articles


This work is licensed under a Creative Commons Attribution 4.0 International License.