- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 4
- Application of Pascal Distribution Series to Ronning Type Starlike and Convex Functions
Application of Pascal Distribution Series to Ronning Type Starlike and Convex Functions
Authors : Gangadharan MURUGUSUNDARAMOORTHY
Pages : 243-251
Doi:10.31197/atnaa.743436
View : 4 | Download : 2
Publication Date : 2020-12-30
Article Type : Research
Abstract : In this article we investigate the connections between the Pascal distribution series and the class of analytic functions $ f $ normalized by $ f ( 0 ) = f ' ( 0 ) - 1 = 0 $ in the open unit disk $ \mathbb { U } = \left \{ z \in \mathbb { C } : | z | < 1 \right \} $ and its coefficients are probabilities of the Pascal distribution.More precisely ,we determine such connection with parabolic starlike and uniformly convex functions in the open unit disk $\mathbb{U}$ .Keywords : Starlike functions, Convex functions, Uniformly Starlike functions, Uniformly Convex functions, Hadamard product, Pascal distribution series