Abstract
Making use of the linear operator Iλm defined by (Frasin 2012), we introduce the class 𝕄p,jm(λ,μ,α) of meromorphically p-valent functions in the punctured unit disk 𝒰∗. Furthermore, we obtain some sufficient conditions for starlikeness and close-to-convexity for functions belonging to this class. Several corollaries and consequences of the main results are also considered.
Highlights
Making use of the linear operator IImλλm de ned by (Frasin 2012), we introduce the class MMmppmppp(λλλ λλλ λλλ of meromorphically pp-valent functions in the punctured unit disk UU∗
We obtain some sufficient conditions for starlikeness and close-to-convexity for functions belonging to this class
We denote by Σ∗ppppp(ααα the class of all meromorphically pp-valent starlike of order δδ
Summary
Making use of the linear operator IImλλm de ned by (Frasin 2012), we introduce the class MMmppmppp(λλλ λλλ λλλ of meromorphically pp-valent functions in the punctured unit disk UU∗. A function ffffff in Σppppp is said to be meromorphically pp-valent starlike of order αα if and only if zzzz′ (zz) ff (zz) A function ffffff in Σppppp is said to be meromorphically pp-valent convex of order αα if and only if zzzz′′ (zz) ff′ (zz) A function ffffff belonging to Σppppp is said to be meromorphically pp-valent close-to-convex of order αα if it satis es ff′ (zz) zz−pppp
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