The growth of entire functions under the q-difference operators is studied inthis paper, and then some properties of Julia set of entire functions under the higher orderq-difference operators are obtained.
In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.
In this paper, we investigate some analytic properties for a class of holomorphic matrix- valued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on C^2×2 and Julia set of one dimensional complex dynamic system.
