this paper uses the tsuji’s characteristic to investigate the uniqueness of transcen- dental meromorphic function with shared values in an angular domain dealing with the multiple values which improve a result of j. zheng.

ABSTRACT. The second fundamental theorem of Nevanlinna concerning meromorphic functions of a complex variable is extended in this note to an analogous result for meromorphic minimal surfaces. A similar extension of the first fundamental theorem involved generalizations of the classical proximity and enumerative functions and also a new visibility function; for the present result, a second enume...

We investigate when differential polynomials in real transcendental meromorphic functions have non-real zeros. For example, we show that if g is a real transcendental meromorphic function, c ∈ R \ {0} and n ≥ 3 is an integer, then g′gn − c has infinitely many non-real zeros. If g has only finitely many poles, then this holds for n ≥ 2. Related results for rational functions g are also considered.

The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences {cn} and {dn} of positive real numbers. By specializing {cn} and {dn}, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined. The theorems presented, in many cases, confirm or ge...

In the paper, we study the normality of families of meromorphic functions related a Hayman Conjecture. We consider whether a family meromorphic functions F is normal in D, if for each function f in F , f ′ + af = b has at most one zero, where n is a positive integer, a and b = 0 are two finite complex numbers. Some examples show that the conditions in our results are best possible.

If f is a meromorphic function in the complex plane, R. Nevanlinna noted that its characteristic function T r, f could be used to categorize f according to its rate of growth as |z| r → ∞. Later H. Milloux showed for a transcendental meromorphic function in the plane that for each positive integer k, m r, f k /f o T r, f as r → ∞, possibly outside a set of finite measure where m denotes the pro...

The main concerned target of this article is to define and study some classes meromorphic function spaces using the general spherical derivatives. Besov-type functions as well normal are considered intensively both compared deeply with each other. Specifically, multiple results concerning meromorphic-type non-normal obtained by help proved constructing specific mild conditions on sequences poin...

A bstract We show that the differential equation for three-loop equal-mass banana integral can be cast into an ? -factorised form with entries constructed from (meromorphic) modular forms and one special function, which given as iterated of meromorphic forms. The allows a systematic solution to any order in dimensional regularisation parameter . alphabet integrals contains six letters.

The Painlevé property is closely connected to differential equations that are integrable via related iso-monodromy problems. Many apparently integrable discrete analogues of the Painlevé equations have appeared in the literature. The existence of sufficiently many finite-order meromorphic solutions appears to be a good analogue of the Painlevé property for discrete equations, in which the indep...