Generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) based some growth properties of composite analytic functions in the unit disc

Year 2022, Volume: 71 Issue: 1, 226 - 236, 30.03.2022

Tanmay Biswas , Chınmay Bıswas

https://doi.org/10.31801/cfsuasmas.952921

Abstract

Our aim in this paper is to introduce some idea about generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) of an analytic function with respect to another analytic function in the unit disc where α and β are continuous non-negative functions on (-∞,+∞). 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 (α,β) and generalized relative Nevanlinna type (α,β) as compared to the growth of their corresponding left and right factors.

Keywords

Growth, analytic function, composition, unit disc, generalized relative Nevanlinna order (α β), generalized relative Nevanlinna type (α β)

References

• Agarwal, A. K., On the properties of an entire function of two complex variables, Canadian J. Math., 20 (1968), 51–57. https://doi.org/10.4153/CJM-1968-007-3
• Biswas, T., Biswas, C., Growth properties of composite analytic functions in unit disc from the view point of their generalized Nevanlinna order (α, β), Aligarh Bull. Math., 39 (1) (2020), 55–64.
• Fuks, B. A., Introduction to the Theory of Analytic Functions of Several Complex Variables, Translations of Mathematical Monographs, Amer. Math. Soc., Providence, Rhode Island, 1963. https://doi.org/10.1090/mmono/008
• Juneja, O. P., Kapoor, G. P., Analytic Functions-Growth Aspects, Research Notes in Mathematics, 104, Boston - London - Melbourne: Pitman Advanced Publishing Program, 296 p, 1985.
• Sheremeta, M. N., Connection between the growth of the maximum of the modulus of an entire function and the moduli of the coefficients of its power series expansion, Izv. Vyssh. Uchebn. Zaved Mat., 2 (1967), 100–108 (in Russian).