‎In this paper‎, ‎we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $Q_p$-classes‎. ‎Also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎Moreover‎, ‎compact composition operators $C_phi$ and Lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $Q_p$-classes are characte...

1 Presented by We construct a function f (z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f * λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample to a result of Greiner and Ruscheweyh.

Abstract In this paper we study some properties of functions f which are analytic and normalized (i.e. $$f(0)=0=f'(0)-1$$ f ( 0 ) = ′ - 1 ) such ...

A version of the second main theorem of Nevanlinna theory is proved, where the ramification term is replaced by a term depending on a certain composition operator of a meromorphic function of small hyper-order. As a corollary of this result it is shown that if n ∈ N and three distinct values of a meromorphic function f of hyper-order less than 1/n have forward invariant pre-images with respect ...

where f is meromorphic and g is entire (g may be meromorphic when f is rational). A nonlinear meromorphic function F (z) is called prime (pseudo prime) if every factorization of form (1) implies that either f is bilinear or g is linear (either f is rational or g is a polynomial). Clearly, a prime function is an analogy of a prime number. Over the past thirty years, many classes of prime or pseu...