Subclass of Analytic Functions Related with Pascal Distribution Series

Abstract

The prime purpose of this article is to derive a necessary and sufficient condition for a linear operator associated with the Pascal distribution series to be in the class T S μ , σ , δ of analytic functions. Moreover, inclusion relation and an integral operator linked to the Pascal distribution series is considered. We have also provided some results as corollaries of our theorems.

Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

“…Several researchers investigated certain subclasses of analytic functions using various probability distributions, such as the Pascal, Poisson, and Borel distributions, (see for example, [23,[46][47][48][49][50]). There have been no previous studies that have investigated a biunivalent class of functions using the q-Pascal distribution series in association with the q-GP using the subordination principle, to the best of the researchers' knowledge.…”

On Miller–Ross-Type Poisson Distribution Series

“…In recent years, several researchers used this distribution series [19,20] and other distribution series such as Poisson distribution series [21][22][23][24][25][26], Pascal distribution series [27][28][29][30], hypergeometric distribution series [31][32][33][34][35][36], and the Mittag-Leffler-type Poisson distribution [37] to obtain some necessary and sufficient conditions for these distributions to belong to certain classes of analytic functions defined in U. In the present paper we obtain some necessary and sufficient conditions for the Miller-Ross-type Poisson distribution series k ε α,c to be in our classes S * T (γ, β) and K T (γ, β).…”

Subclass of analytic functions with negative coefficients related with Miller-Ross-type Poisson distribution series

“…In recent years, several researchers have obtained some necessary and sufficient conditions for functions belong to certain classes of univalent function using distribution series such as Poisson distribution series [7,16,15,29,30,32], Pascal distribution series [5,10,17,19,34], the confluent hypergeometric distribution series [9,22,24,35,37,41], and the Mittag-Leffler-type Poisson distribution series [1,21]. Motivated with the works mentioned, in the present paper we determine a necessary and sufficient condition for K m ν,c to be in our class W δ (α, γ, β).…”