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Generalized relative Nevanlinna order \((\alpha,\beta)\) and generalized relative Nevanlinna type \((\alpha,\beta)\) based some growth properties of composite analytic functions in the unit disc. (English) Zbl 1489.30041

Summary: Our aim in this paper is to introduce some idea about generalized relative Nevanlinna order \((\alpha,\beta)\) and generalized relative Nevanlinna type \((\alpha,\beta)\) of an analytic function with respect to another analytic function in the unit disc where \(\alpha\) and \(\beta\) are continuous non-negative functions on \((-\infty,+\infty)\). So we discuss about some growth properties relating to the composition of two analytic functions in the unit disc on the basis of generalized relative Nevanlinna order \((\alpha,\beta)\) and generalized relative Nevanlinna type \((\alpha,\beta)\) as compared to the growth of their corresponding left and right factors.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30B10 Power series (including lacunary series) in one complex variable
30J99 Function theory on the disc
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