The purpose of this paper is to introduce two novel subclasses Γλ n, α, β and Γλ n, α, β of meromorphic p-valent functions by using the linear operator D λ . Then we prove the necessary and sufficient conditions for a function f in order to be in the new classes. Further we study several important properties such as coefficients inequalities, inclusion properties, the growth and distortion theo...

and Applied Analysis 3 2. Some Properties of the Classes ∑∗ λ p, n, α and ∑λ c p, n, α Theorem 2.1. If f z ∈ ∑ p, n satisfies ∣ ∣ ∣ ∣ ( zf z )eiλ/ p−α cosλ { e zf ′ z f z α cosλ ip sinλ } ( p − α cosλ ∣ ∣ ∣ ∣ < n √ n2 1 ( p − α cosλ z ∈ U , 2.1 then f z ∈ ∑∗λ p, n, α . Proof. Let us set a function h z by h z 1 z ( zf z )eiλ/ p−α cosλ 1 z ean ( p − α cosλ n · · · 2.2 for f z ∈ ∑ p, n . Then clea...

The authors would like to thank the referees for their helpful suggestions which essentially improved the presentation of this paper. Abstract. In this paper, we introduce a new subclass of meromorphic functions and investigate inclusion relationships and properties of a certain class of meromorphically p-valent functions, which are defined by means of the familiar operator involving the genera...

It is well-known that the classes of starlike, convex and close-to-convex univalent functions are closed under convolution with convex functions. In this paper, closure properties under convolution of general classes of meromorphic p-valent functions that are either starlike, convex or close-to-convex with respect to n-ply symmetric, conjugate and symmetric conjugate points are investigated. 20...

For certain meromorphic p-valent functioun φ andψ, we study a class of functioun f (z) = 1 zp + ∑∞ n=p anz n, (an ≥ 0), defined in the punctured unit disc D, satisfying R ( (f∗φ)(z) (f∗ψ)(z) ) > α (0 ≤ α ≤ 1, z ∈ D) . Coeffiicient etimate disortion theorem and radii of starlikeness and convexity are obtained. Further we consider integral operators associated with functions belonging to the afor...