Abstract
The aim of this article is to introduce and study certain subclasses of analytic functions and we investigate various properties of these classes such as inclusion properties and convex convolution preserving properties. Also, some related applications are discussed.
Highlights
Let A be the class of analytic functions of the form
If f and g are analytic in E, we say that f is subordinate to g, written f ≺ g or f (z) ≺ g(z), if there exists a schwartz function w in E such that f (z) = g(w(z))
A function f ∈ A is said to be in the class Mμδ(Φ, ξ, H), if and only if, Jδ(f (z)) ∈ Pμ(H), where φ∗ξ∗f φ∗f
Summary
Keywords and phrases: close-to-convex functions, Noor integral operator, Janowski’s functions, conic domains. Analytic functions p in the class P [A, B] can be defined by using subordination as follows [5]. A function f ∈ A is said to be in the class Mμδ(Φ, ξ, H), if and only if, Jδ(f (z)) ∈ Pμ(H), where φ∗ξ∗f φ∗f. A function f ∈ A is said to be in the class CMμδ,θ(Φ, ξ, G, H), if there exists a function g ∈ Wθ(Φ, ξ, H) such that φ∗ξ∗f φ∗f. A function f ∈ A is said to be in class Tμ(φ, G, H) if there exists a function g ∈ S∗(φ, G) such that z(φ ∗ f ) (φ ∗ g) ∈ Pμ (H) Analogous to this class in terms of Alexander type relation, we can define the class Tμ∗(φ, G, H) as following. For different values of μ, φ, G and H, we can obtain the well-known classes, referred as [4, 8, 13, 15, 16, 23]
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