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This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of ℂ n .

Chen and Gu [1] have given some results relating to normal families, and, in this paper, we give versions of these results valid for normal functions. In the process, we improve some of our previous results involving products of certain spherical derivatives as they relate to normal functions. Some examples are given to show the sharpness of our results.

In this paper we improve and generalise a result of J. Clunie by proving that if f(z) is a transcendental integral function with only zeros of order at least k + 1, then f(k)(z) assumes every finite non-zero complex value infinitely often. Also, the related criterion for normality of a family of holomorphic functions is given, and the value distribution of f2 + afk is discussed.

We prove the existance of a kind of singular directions concerning the differential polynomials\(f^{(k)} + \sum\limits_{j = 0}^{k - 1} {a_j f^{(j)} - af^n } \).

We give a simple description of boundary sets which may be ignored in calculating the maximum of subharmonic or plurisubharmonic functions.