ON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS ASSOCIATED WITH PASCAL DISTRIBUTION SERIES

ON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS ASSOCIATED WITH PASCAL DISTRIBUTION SERIES

K. Marimuthu, J. Uma

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Abstract

In this study, we establish a relation between particular subclasses of complex order univalent functions and Pascal distribution series. The main aim of the present investigation is to obtain the necessary and su cient conditions for Pascal distribution series Fj q ( ) belongs to the classes S( ;  ;  ) and R( ;  ;  ). We also provide some properties of integral operator connected to Pascal distribution series and adequate conditions for Pj q ( ) to be in K( ;  ) and R( ;  ). Also, we discuss some corollaries and consequences of the major results.

Keywords

Complex order, Pascal distribution, Integral operator, Univalent function.