## 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

### MSC:

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

### References:

  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.  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.  Bergweiler, W., On the Nevanlinna characteristic of a composite function, Complex Variables Theory Appl., 10 (1988), 225-236. · Zbl 0628.30035  Biswas, T., On some inequalities concerning relative (p, q)-ϕ type and relative (p, q)-ϕ weak type of entire or meromorphic functions with respect to an entire function, J. Class. Anal., 13(2) (2018), 107-122. · Zbl 1424.30107  Biswas, T. and Biswas, C., Generalized order (α, β) oriented some growth properties of composite entire functions, Ural Math. J., 6(2) (2020), 25-37. · Zbl 1462.30052  Biswas, T. and Biswas, C. and Biswas, R., A note on generalized growth analysis of composite entire functions, Poincare J. Anal. Appl., 7(2) (2020), 277-286.  Biswas, T. and Biswas, C., Some results on generalized relative order (α, β) and generalized relative type (α, β) of meromorphic function with respective to an entire function, Ganita, 70(2) (2020), 239-252.  Chyzhykov, I. and Semochko, N., Fast growing entire solutions of linear dif-ferential equations, Math. Bull. Shevchenko Sci. Soc., 13 (2016), 68-83. · Zbl 1374.34362  Hayman, W. K., Meromorphic Functions, The Clarendon Press, Oxford, 1964. · Zbl 0115.06203  Juneja, O. P., Kapoor, G. P. and Bajpai, S. K., On the (p, q) -order and lower (p, q)-order of an entire function, J. Reine Angew. Math., 282 (1976), 53-67. · Zbl 0321.30031  Laine, I., Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993.  Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411-414. · Zbl 0109.30104  Shen, X., Tu, J. and Xu, H. Y., Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q] -ϕ order, Adv. Difference Equ. 2014(1): 200, (2014), 14 p., http://www.advancesindifferenceequations. com/content/2014/1/200. · Zbl 1417.30022  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).  Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, New York, 1949.  Yang, L., Value distribution theory, Springer-Verlag, Berlin, 1993. · Zbl 0790.30018
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.