Certain Class of Analytic Functions Connected with  q -Analogue of the Bessel Function

Nazek Alessa,B Venkateswarlu,T.S Karthik,K Loganathan,G Sujatha,P Thirupathi Reddy

doi:10.1155/2021/5587886

Abstract

The focus of this article is the introduction of a new subclass of analytic functions involving q-analogue of the Bessel function and obtained coefficient inequities, growth and distortion properties, radii of close-to-convexity, and starlikeness, as well as convex linear combination. Furthermore, we discussed partial sums, convolution, and neighborhood properties for this defined class.

Highlights

Indicated by S, the subclass of A is composed of functions that are univalent in Δ
E intense devotion of scientists has recently fascinated the study of the q-calculus. e great focus in many fields of mathematics and physics is due to its benefits
In the analysis of many subclasses of analytic functions, the importance of the q-derivative operator Dq is very evident from its applications

Summary

Introduction

In the analysis of many subclasses of analytic functions, the importance of the q-derivative operator Dq is very evident from its applications. E mathematical description and applications of the fractional q-calculus and fractional q-derivative operators in geometric function theory were systematically investigated in this surveycum-expository analysis article [4]. El-Deeb and Bulboaca [18] introduced the linear operator using the definition of q-derivative along with the idea of convolutions Nl℘,q: A ⟶ A defined by. We propose a new subclass φl℘,q(Z, θ) of A concerning q- analogue of the Bessel function as follows. 2. Coefficient Inequalities is section gives us an adequate requirement for a function η given by (1) to be in φl℘,q(Z, θ). If η ∈ Tφl℘,q(Z, θ), the function ρ(w) w􏼐Nl℘,qη(w)N􏼑′ l℘+,qZηw(w2􏼐)Nl℘,qη(w)􏼑′′, w ∈ Δ, (22).

Distortion Theorem

Radii of Close-to-Convexity and Starlikeness

Partial Sums

Neighborhood Property