In this paper, by meromorphic functions we will always mean meromorphic functions in the complex plane C. We adopt the standard notations of the Nevanlinna theory of meromorphic functions as explained in [6]. It will be convenient to let E denote any set of positive real numbers of finite linear measure, not necessarily the same at each occurrence. For a non-constant meromorphic function h, we ...

A normalized univalent function f is called Ma–Minda starlike or convex if zf ðzÞ=f ðzÞ uðzÞ or 1þ zf ðzÞ=f 0ðzÞ uðzÞ where u is a convex univalent function with uð0Þ 1⁄4 1. The class of Ma–Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and clo...

Let f be a non-constant meromorphic function, n, k be two positive integers and a(z)( 6≡ 0,∞) be a meromorphic small function of f . Suppose that f − a and (f)−a share the value 0 CM. If either (1) n ≥ k+1 and N(r,∞; f) = S(r, f), or (2) n > k + 1 and N(r,∞; f) = λ T (r, f)(λ ∈ [0, 1)), then f ≡ (f) and f assume the form f(z) = ce λ n , where c is a nonzero constant and λ = 1. This result shows...

For a germ of a meromorphic function f = P Q , we offer notions of the mono-dromy operators at zero and at infinity. If the holomorphic functions P and Q are non-degenerated with respect to their Newton diagrams, we give an analogue of the formula of Varchenko for the zeta-functions of these monodromy operators. A polynomial f of (n + 1) complex variables of degree d determines a meromorphic fu...

The purpose of the present paper is to give some characterizations for a Gaussian hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.

The objective of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.

Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , N r, f , and m r, f see, e.g., 1, 2 . The notation S r, f is defined to be any quantity satisfying S r, f o T r, f as r → ∞ possibly outside a set of E of finite linear measure. Let F be a family of meromorphi...

In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.

Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L zeta function of Y and computes examples. When π = Z, the L zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta fun...

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.