Properties of Sakaguchi Kind Functions Associated with Bessel Function

H.Priya H.Priya,B Srutha Keerthi

doi:10.13189/ms.2021.090617

Abstract

The aim of the paper is to obtain the First Hankel Determinant and the Second Hankel determinant. We shall make use of few lemmas which are based on Caratheodory's class of analytic functions. We establish a new Sakaguchi class <img src=image/13424969_01.gif> of univalent function, further we estimate the sharp bound for initial coefficients <img src=image/13424969_02.gif> and <img src=image/13424969_03.gif> using the Bessel function expansion. We have discussed about the coefficient <img src=image/13424969_04.gif> as well for the Second Hankel Determinant. The results are obtained for Sakaguchi kind. Our results travel along exploring the stages of Hankel Determinants. Various types of technologies like wire, optical or other electromagnetic systems are used for the transmission of data in one device to another. Filters play an important role in the process that can remove disorted signals. By using different parameter values for the function belongs to Sakaguchi kind of functions the Low pass filter and High pass filter can be designed and that can be done by the coefficient estimates.

Highlights

IntroductionLet A denote the class of analytic functions of the form:. κ=2 and S be the subclass of A which are univalent in U
Let A denote the class of analytic functions of the form: ∞f (ξ) = ξ + aκξκ, ξ ∈ U = {ξ ∈ C : |ξ| < 1} (1)κ=2 and S be the subclass of A which are univalent in U
Of univalent function, further we estimate the sharp bound for initial coefficients a2 and a3 using the Bessel function expansion

Summary

Introduction

Let A denote the class of analytic functions of the form:. κ=2 and S be the subclass of A which are univalent in U. Let A denote the class of analytic functions of the form:. If the function F is univalent in U, the following holds (see [1] and [2]):. For the conditions ν > 0, λ > −1, and 0 < q < 1, we can define the function Iνλ,q : U → C by; Iνλ,q (ξ ). (ν > 0, λ > −1, 0 < q < 1, 0 ≤ ρ ≤ 1, |t| ≤ 1 but t = 1) In this paper, we obtain the Fekete-Szego inequalities and Second Hankel Determinant for the function of the class Mνλ,q(ρ, t, Ψ)

First Hankel Dterminant Problem

C12 2B1

Conclusion