Abstract
In this paper we establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized order \((\alpha ,\beta )\) and generalized lower order \((\alpha ,\beta )\) where \(\alpha \) and \(\beta \) are continuous non-negative functions on \((-\infty ,+\infty )\).
Highlights
Known resultsWe present some lemmas which will be needed in the sequel
We denote by C the set of all finite complex numbers
Several authors made close investigations on the properties of entire functions related to the generalized order (α, β) in some different direction
Summary
We present some lemmas which will be needed in the sequel. Let b satisfy 0 < b < 1 and c(b) = (1 − b)2/(4b). For all sufficiently large values of r, we have. Mf (c(b)Mg(br)) ≤ Mf◦g(r) ≤ Mf (Mg(r)). In addition if b = 1/2, for all sufficiently large values of r, the inequality is true. If f and g are any two entire functions. For all sufficiently large values of r, the estimate is true μf ◦g (r)
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