Hypergeometric functions in the parabolic starlike and uniformly convex domains

Geometric Properties of Generalized Struve Functions

“…Many authors have determined sufficient conditions on the parameters of these functions for belonging to a certain class of univalent functions, such as convex, starlike, close-to-convex, etc. Someone can find more information about geometric properties of special functions in [2,3,4,11,15,16,17,18,14]. In this present investigation our goal is to determine conditions of univalence, starlikeness, convexity and close-to-convexity of generalized Struve functions.…”

Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator

“…Differentiating both sides of Equation (19) logarithmically with respect to z and using the identity (5), we get…”

“…In recent years, several authors obtained many interesting results involving the DziokSrivastava linear operator H l,m p (α 1 ) (see [1], [4] to [9], [11], [15], [16], [19], and [23] [2,3,14,17,20,21,24]. Here, and elsewhere in this investigation, we make the notation simple by writing…”

On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

“…Motivated by results on connections between various subclasses of analytic univalent functions by using hypergeometric functions (see, for example, [4,8,15,23,24])), and the work done in [12,16,17,18], we determine necessary and sufficient conditions for zu p (z) to be in SP p (α, β) and UCSP(α, β) and also give necessary and sufficient conditions for z(2 − u p (z)) to be in the function classes SP p T (α, β) and UCSPT (α, β). Furthermore, we give necessary and sufficient conditions for I(κ, c)f to be in UCSPT (α, β) provided that the function f is in the class R τ (A, B).…”