Abstract
In this paper, the Jackson q-derivative is used to investigate two classes of analytic functions in the open unit disc. The coefficient conditions and inclusion properties of the functions in these classes are established by convolution methods.
Highlights
Let B be the class of functions that are analytic and of the form: ∞ f (z) = z +Citation: Lashin, A.M.Y.; Algethami, Properties of Certain Classes of (z ∈ E := {z ∈ C : |z| < 1}). (1) k =2B.M.; Badghaish, A.O
We introduced and studied two new subclasses of analytic functions in the open unit disc using the Jackson q-derivative
A similar technique to that given by Silverman et al [1] was used to obtain certain convolution properties for these two classes
Summary
Let B be the class of functions that are analytic and of the form:. Citation: Lashin, A.M.Y.; Algethami, Properties of Certain Classes of (z ∈ E := {z ∈ C : |z| < 1}). ∑ ak zk , The Hadamard product (or convolution ) of two functions f , g ∈ B , denoted by f ∗ g, is defined by Jackson q-Derivative. Characterizations of convex, starlike and spiral-like functions in terms of convolutions. For each of these classes χ, they determined a function g that depends on χ, such that z ( f ∗ g ) 6 = 0. For q ∈ (0, 1), the Jackson q-derivative of a function f ∈ B is given by (see [9,10]). With the help of the Salagean q-differential operator Ωnq given by (5), we have the following definition. The coefficient conditions and inclusion properties of the functions in these classes are established
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