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On the \((p, q)\)th relative order oriented growth properties of entire functions. (English) Zbl 1474.30231

Summary: The relative order of growth gives a quantitative assessment of how different functions scale each other and to what extent they are self-similar in growth. In this paper for any two positive integers \(p\) and \(q\), we wish to introduce an alternative definition of relative \((p, q)\)th order which improves the earlier definition of relative \((p, q)\)th order as introduced by B. K. Lahiri and D. Banerjee [Soochow J. Math. 31, No. 4, 497–513 (2005; Zbl 1090.30031)]. Also in this paper we discuss some growth rates of entire functions on the basis of the improved definition of relative \((p, q)\)th order with respect to another entire function and extend some earlier concepts as given by Lahiri and Banerjee [loc. cit.], providing some examples of entire functions whose growth rate can accordingly be studied.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D15 Special classes of entire functions of one complex variable and growth estimates

Citations:

Zbl 1090.30031
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References:

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