We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....

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...