In this paper, we employ Nevanlinna’s value distribution theory to investigate the existence of meromorphic solutions of some algebraic differential equations. We obtain the representations of all meromorphic solutions of certain algebraic differential equations with constant coefficients and dominant term. Many results are the corollaries of our result, and we will give the complex method to f...

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...

Let M be a Riemannian manifold. For p ∈ M , the tensor algebra of the negative part of the (complex) affinization of the tangent space of M at p has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over M with a connection. We construct a sheaf V of meromorphic open-string vertex algebras on the sheaf of parallel...

In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained five results which will improve all the existing results. Key word and phrases: Meromorphic functions, uniqueness, weighted sharing, derivative, shared set.

In this paper, we investigate the iterated order of meromorphic solutions of homogeneous and nonhomogeneous linear differential equations where the coefficients are meromorphic functions satisfying certain growth conditions. And some estimates of iterated convergence exponent are also given. 2000 Mathematics Subject Classification: 34M10, 30D35

Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan √ 8 ≈ 7032 . If in addition all critical points of the function are multiple, then a similar statement holds with π/2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f (k) + A(z)f = 0, k ≥ 2, where A(z) is a transcendental meromorphic function with ρp(A) = ρ > 0 and meromorphic functions of finite iterated p−order.

In this paper, we investigate the growth and fixed points of meromorphic solutions of higher order nonhomogeneous linear differential equations with meromorphic coefficients and their derivatives. Our results extend greatly the previous results due to J. Wang and I.Laine, B. Beläıdi and A. Farissi.

In the present investigation, the authors derive necessary and sufficient conditions for spirallikeness and convex spirallikeness of a suitably normalized meromorphic p-valent function in the punctured unit disk, using convolution. Also we give an application of our result to obtain a convolution condition for a class of meromorphic functions defined by a linear operator.

Making use of the principle of subordination between analytic functions and a family of integral operators defined on the space of meromorphic functions, we introduce and investigate some new subclasses of meromorphic functions. Such results as inclusion relationships and integralpreserving properties associated with these subclasses are proved. Several subordination and superordination results...