Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions
Open Access
- 23 March 2021
- journal article
- Published by Earthline Publishers in Earthline Journal of Mathematical Sciences
- Vol. 6 (2), 271-292
- https://doi.org/10.34198/ejms.6221.271292
Abstract
The purpose of this article is to derive the necessary and sufficient conditions for the power series 〖P℘〗_(ℷ,γ)^μ (t) whose coefficients are probabilities of the beta negative binomial distribution to be in the family F(σ,τ,ϵ,η,μ,ℷ,γ) of holomorphic functions which are defined in the open unit disk. We establish a number of important geometric properties, such as, coefficient estimates, extreme points, neighborhood property, integral representation, radii of starlikeness and convexity and Hadamard product properties for functions belongs to this family. Also we determinate some differential subordination properties of the power series 〖P℘〗_(ℷ,γ)^μ (t).Keywords
This publication has 22 references indexed in Scilit:
- Some subordination and superordination results associated with generalized Srivastava-Attiya operatorFilomat, 2017
- Some Properties of a New Class of Univalent Functions Involving a New Generalized Differential Operator with Negative CoefficientsIndian Journal of Science and Technology, 2016
- Some Properties of the Class of Univalent Functions with Negative CoefficientsApplied Mathematics, 2012
- On a Univalent Class Involving Differential Subordinations with ApplicationsJournal of Mathematics and Statistics, 2011
- Sufficient conditions for strongly star-like functions involving the generalized Srivastava–Attiya operatorIntegral Transforms and Special Functions, 2011
- Differential subordination and superordination of analytic functions defined by the Dziok–Srivastava linear operatorJournal of the Franklin Institute, 2010
- Sandwich Theorems for Certain Subclasses of Analytic Functions Defined by Family of Linear OperatorsJournal of Applied Analysis, 2009
- Subordination and Superordination Results for a Class of Analytic Multivalent FunctionsInternational Journal of Mathematics and Mathematical Sciences, 2008
- Argument estimates of certain analytic functions defined by a class of multiplier transformationsMathematical and Computer Modelling, 2003
- Univalent functions and nonanalytic curvesProceedings of the American Mathematical Society, 1957