Some Sufficient Conditions for Generalized Bessel Functions Associated with Conic Regions

Porwal, Saurabh; Ahmad, Moin

doi:10.1007/s10013-014-0089-8

Cited by 8 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Inspired by the findings presented in references [31,32], our objective is to establish sufficient conditions for the parameter of the normalized Bessel function of the first kind. To initiate our discussion, let us revisit the definition of the generalized Bessel function of the first kind.…”

Section: Definition 3 ([25]mentioning

confidence: 99%

See 1 more Smart Citation

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

Mondal,

Giri,

Kondooru

2024

Symmetry

View full text Add to dashboard Cite

Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are imposed on the parameters to ensure the inclusion of the confluent hypergeometric function within the analytic function class. The coefficient bound of the class is used to determine the inclusion properties of integral operators involving generalized Bessel functions of the first kind. Different results are observed for these operators, depending on the specific values of the parameters. The results presented here include some previously published findings as special cases.

show abstract

Section: Definition 3 ([25]mentioning

confidence: 99%

“…where r < 0, t p > 1 and t p ̸ = 0, −1, −2, • • • . For f (z) ∈ A, using a convolution operator H t p ,r ( f )(z) is defined as (see [32])…”

Section: Definition 3 ([25]mentioning

confidence: 99%

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

Mondal,

Giri,

Kondooru

2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…Motivated by results on connections between various subclasses of analytic univalent functions by using hypergeometric functions and generalized Bessel functions (see [5,6,8,10,11,13]), we establish a number of connections between the classes…”

Section: An Application Of Certain Convolution Operator Involving Poimentioning

confidence: 99%

An application of certain convolution operator involving Poisson distribution series

Porwal

2016

Asian-European J. Math.

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise, we investigate such connections with the classes of analytic univalent functions [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in the open unit disc [Formula: see text].

show abstract

“…Applications of hypergeometric functions [6], generalized hypergeometric functions [7], confuent hypergeometric functions [8], generalized Bessel functions [9,10], Wright function [11], and Fox-Wright function [12] are crucial to the development of geometric function theory. Derivations of specifc geometric properties were recently conducted in [13,14] to build links between geometric function theory and statistics by using a generalized discrete probability distribution.…”

Section: Introductionmentioning

confidence: 99%

Geometric Properties of Analytic Functions Defined by the (p, q) Derivative Operator Involving the Poisson Distribution

Santhiya

Thilagavathi

2023

Journal of Mathematics

View full text Add to dashboard Cite

The objective of the current paper is to find the necessary and sufficient condition for the function to belong to the subclass of C d , δ , μ , β of analytic functions involving the Poisson distribution defined by the p , q derivative operator. Furthermore, distortion bounds, covering theorems, a radius of starlikeness, and convexity for functions belonging to this class are obtained.

show abstract

Some Sufficient Conditions for Generalized Bessel Functions Associated with Conic Regions

Cited by 8 publications

References 12 publications

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

An application of certain convolution operator involving Poisson distribution series

Geometric Properties of Analytic Functions Defined by the (p, q) Derivative Operator Involving the Poisson Distribution

Contact Info

Product

Resources

About