Biswas, Tanmay; Biswas, Chınmay 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 Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 71, No. 1, 226-236 (2022). 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 Keywords:growth; analytic function; composition; unit disc; generalized relative Nevanlinna order \((\alpha,\beta)\); generalized relative Nevanlinna type \((\alpha,\beta)\) PDFBibTeX XMLCite \textit{T. Biswas} and \textit{C. Biswas}, Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 71, No. 1, 226--236 (2022; Zbl 1489.30041) Full Text: DOI References: [1] 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 · Zbl 0185.33201 [2] 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. · Zbl 1513.30137 [3] 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 · Zbl 0138.30902 [4] 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. · Zbl 0582.30001 [5] 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). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.