Necessary and sufficient conditions for hypergeometric functions to be in a subclass of analytic functions

Subclasses of analytic functions associated with Pascal distribution series

“…Email address: bafrasin@yahoo.co (Basem Aref Frasin) and f ∈ C(k, λ) if and only if zf ∈ S(k, λ).The class S(k, λ) was studied by Frasin et al [7]. We note that S(k, 0) = S(k) and C(k, 0) = C(k), where the classes S(k) and C(k) were introduced and studied by Padmanabhan [17] (see also, [11], [16]) .…”

“…Motivated by several earlier results on connections between various subclasses of analytic and univalent functions, by using hypergeometric functions (see for example, [2,7,10,19,20]) and by using various distributions such as Yule-Simon distribution, Logarithmic distribution, Poisson distribution, Binomial distribution, Beta-Binomial distribution, Zeta distribution, Geometric distribution and Bernoulli distribution (see for example, [4,6,8,9,12,13,18,15]), in this paper, we determine the necessary and sufficient conditions for Φ m q (z) to be in our classes S(k, λ) and C(k, λ) and connections of these subclasses with R τ (A, B). Finally, we give conditions for the integral operator…”

A Generalized Subclass of Starlike Functions Involving Jackson’s ( p, q)  Derivative

“…Some interesting corollaries and natural consequences of the main findings are also considered. Some important techniques used earlier by many researchers were applied in this work (see Al-Hawary et al [11,12], Aouf and Srivastava [13], and Frasin et al [14][15][16][17][18][19]).…”

On a Harmonic Univalent Subclass of Functions Involving a Generalized Linear Operator

“…where I m δ,µ,λ,η,ς,τ f (z) is defined by (4). For relevant and recent references related to this work, we refer the reader to [13][14][15][16][17][18][19][20].…”