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

Authors : Gangadharan MURUGUSUNDARAMOORTHY

Pages : 243-251

Doi:10.31197/atnaa.743436

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Publication Date : 2020-12-30

Article Type : Research Paper

Abstract : In  this  article  we  investigate  the  connections   between  the  Pascal  distribution  series and   the  class  of  analytic  functions   $ f $   normalized  by  $ f insert ignore into journalissuearticles values( 0 ); = f ` insert ignore into journalissuearticles values( 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