Application of Pascal Distribution Series to Ronning Type Starlike and Convex Functions

Year 2020, Volume: 4 Issue: 4, 243 - 251, 30.12.2020

Gangadharan Murugusundaramoorthy

https://doi.org/10.31197/atnaa.743436

Cited By: 2

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

Supporting Institution

NOT APPLICALE

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