On some growth properties of composite entire and meromorphic functions From the view point of their generalized type \((\alpha,\beta)\) and generalized weak type \((\alpha,\beta)\). (English) Zbl 1499.30268

Biswas, Tanmay; Biswas, Chinmay

South East Asian J. Math. Math. Sci. 17, No. 1, 31-44 (2021).

MSC:

30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D30	Meromorphic functions of one complex variable (general theory)

Keywords:

entire function; meromorphic function; growth; generalized order \((\alpha, \beta)\); generalized type \((\alpha, \beta)\); generalized weak type \((\alpha, \beta)\)

References:

[1]	Remark 15. In Theorem 5, if we replace the conditions “τ (α 2 ,β 2 ) [g] < ∞” and “0 < τ (α 1 ,β 1 ) [f ] < ∞” by “τ (α 2 ,β 2 ) [g] < ∞” and “0 < τ (α 1 ,β 1 ) [f ] < ∞” respectively and other conditions remain same, then Theorem 5 remains valid with “τ (α 2 ,β 2 ) [g] ” and “τ (α 1 ,β 1 ) [f ]” instead of “τ (α 2 ,β 2 ) [g]” and “τ (α 1 ,β 1 ) [f ]” respectively. Remark 16. In Theorem 5, if we replace the conditions “0 < λ (α 1 ,β 1 ) [f ] ≤ ρ (α 1 ,β 1 ) [f ] < ∞” and “0 < τ (α 1 ,β 1 ) [f ] < ∞” by “0 < λ (α 1 ,β 1 ) [f ] < ∞ ” and “0 < τ (α 1 ,β 1 ) [f ] < ∞” respectively and other conditions remain same, then The-orem 5 remains valid with “λ (α 1 ,β 1 ) [f ]” and “τ (α 1 ,β 1 ) [f ]” instead of “ρ (α 1 ,β 1 ) [f ] ” and “τ (α 1 ,β 1 ) [f ]” respectively.
[2]	Remark 17. In Theorem 5, if we replace the condition “0 < τ (α 1 ,β 1 ) [f ] < ∞” by “0 < τ (α 1 ,β 1 ) [f ] < ∞ ” and other conditions remain same, then Theorem 5 re-mains valid with “limit superior” and “τ (α 1 ,β 1 ) [f ]” instead of “limit inferior” and “τ (α 1 ,β 1 ) [f ]” respectively.
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