Article
KYUNGPOOK Math. J. 2019; 59(2): 301-314
Published online June 23, 2019
Copyright © Kyungpook Mathematical Journal.
Pascal Distribution Series Connected with Certain Subclasses of Univalent Functions
Sheeza M. El-Deeb*,Teodor Bulboacă, Jacek Dziok
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
e-mail : shezaeldeeb@yahoo.com
Faculty of Mathematics and Computer Science, Babe¸s-Bolyai University, 400084 Cluj-Napoca, Romania
e-mail : bulboaca@math.ubbcluj.ro
Faculty of Mathematics and Natural Sciences, University of Rzeszow, 35-310 Rzeszow, Poland
e-mail : jdziok@ur.edu.pl
Received: November 5, 2018; Revised: March 13, 2019; Accepted: March 18, 2019
The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.