Abstract
We study some comparative growth properties of composite entire and meromorphic functions on the basis of their relative orders (relative lower orders).
Highlights
Let f be meromorphic and g be an entire function defined in the open complex plane C
We study some comparative growth properties of composite entire and meromorphic functions on the basis of their relative orders
The maximum modulus function corresponding to entire g is defined as Mg(r) = max{|g(z)| : |z| = r}
Summary
Let f be meromorphic and g be an entire function defined in the open complex plane C. Bernal [1, 2] introduced the definition of relative order of an entire function f with respect to another entire function g, denoted by ρg(f) to avoid comparing growth just with exp z as follows: ρg (f). One can define the relative lower order of a meromorphic function f with respect to an entire function g denoted by λg(f) as follows: lirm→i∞nf log (10). It is known (cf [4]) that if g(z) = exp z Definition 3 coincides with the classical definition of the order of a meromorphic function f. We do not explain the standard definitions and notations of the theory of entire and meromorphic functions as those are available in [6, 7]
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