Abstract
The purpose of the present paper is to introduce several new classes of analytic functions defined by using the Choi-Saigo-Srivastava operator associated with the Dziok-Srivastava operator and to investigate various inclusion properties of these classes. Some interesting applications involving classes of integral operators are also considered.
Highlights
Let Ꮽ denote the class of functions of the form ∞f (z) = z + akzk k=2 (1.1)which are analytic in the open unit disk U = {z : z ∈ C and |z| < 1}
If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f (z) ≺ g(z), if there exists a Schwarz function w, analytic in U with w(0) = 0 and |w(z)| < 1 (z ∈ U), such that f (z) = g(w(z)) (z ∈ U)
For 0 ≤ η, β < 1, we denote by ∗(η), (η), and Ꮿ(η,β) the subclasses of Ꮽ consisting of all analytic functions which are, respectively, starlike of order η, convex of order η, close-to-convex of order η, and type β in U
Summary
If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f (z) ≺ g(z), if there exists a Schwarz function w, analytic in U with w(0) = 0 and |w(z)| < 1 (z ∈ U), such that f (z) = g(w(z)) (z ∈ U). If the function g is univalent in U, the above subordination is equivalent to f (0) = g(0) and f (U) ⊂ g(U). For various other interesting developments involving functions in the class Ꮽ, the reader may be referred (for example) to the work of Srivastava and Owa [1]. Let ᏺ be the class of all functions φ which are analytic and univalent in U and for which φ(U) is convex with φ(0) = 1 and Re{φ(z)} > 0 for z ∈ U
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