Starlike and convex properties for Poisson distribution series

Abstract

Abstract. In this paper, we find the necessary and sufficient conditions, inclusion relations for Poisson distribution series belonging to the classes S * (α, β) and C * (α, β). Further, we consider an integral operator related to Poisson Distribution series. Mathematics Subject Classification (2010): 30C45.

An Application of Pascal Distribution Series on Certain Analytic Functions Associated with Stirling Numbers and Sălăgean Operator

“…In recent years, many researchers have examined some important features in the geometric function theory, such as coefficient estimates, inclusion relations, and conditions of being in some known classes, using different probability distributions such as the Poisson, Pascal, Borel, Mittag-Leffler-type Poisson distribution, etc. (see, for example, [6][7][8][9][10]).…”

“…Motivated by several earlier results on connections between various subclasses of analytic and univalent functions, using hypergeometric functions, generalized Bessel functions, Struve functions, Poisson distribution series, and Pascal distribution series (see, for example, [12], [13][14][15], [7][8][9][16][17][18][19][20][21][22][23], [24]), we determine a necessary and sufficient condition for Υ m σ (z) to be in our class P k (λ, α). Furthermore, we give sufficient conditions for…”

Subclass of Analytic Functions Related with Pascal Distribution Series

“…Several results on the engagements between different subclasses of analytic univalent functions and special functions or distribution series have been studied in the literature (see for example, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]). Herein, we provide a necessary and sufficient condition for Υ t r (ξ) to be in the aforementioned class TS(μ, σ, δ) and investigate an inclusion property of the class TS(μ, σ, δ) associated with the operator I t r f. Ultimately, we provide conditions for the integral operator…”

Certain subclasses of analytic functions associated with Mittag–Leffler-type Poisson distribution series

“…Motivated by results on connections between various subclasses of analytic univalent functions using hyper-geometric functions [7,16], generalized Bessel functions [15], Poisson distribution series [2,8,12], hyper-geometric distribution series [1], confluent hyper-geometric distribution series [17], Binomial distribution series [9] and generalized distribution series [13] also one can refer [2, 6, 8, 10-14, 16, 19, 20] and the references there in this paper we obtain some necessary and sufficient conditions for Kðm; a; bÞ and Kðm; a; b; f Þ belong to the class Kðk; dÞ.…”