Some generalized growth properties of composite entire and meromorphic functions. (English) Zbl 1475.30080

Biswas, Tanmay; Biswas, Chinmay

Korean J. Math. 29, No. 1, 121-136 (2021).

Summary: In this paper we wish to prove some results relating to the growth rates of composite entire and meromorphic functions with their corresponding left and right factors on the basis of their generalized order \((\alpha,\beta)\) and generalized lower order \((\alpha,\beta)\), where \(\alpha\) and \(\beta\) are continuous non-negative functions defined on \((-\infty ,+\infty)\).

MSC:

30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D30	Meromorphic functions of one complex variable (general theory)
30D20	Entire functions of one complex variable (general theory)

Keywords:

entire function; meromorphic function; composition; growth

References:

[1]	W. Bergweiler, On the Nevanlinna Characteristic of a composite function, Complex Variables 10 (1988), 225-236. · Zbl 0628.30035
[2]	T. Biswas and C. Biswas, Some results on generalized relative order (α,β) and generalized relative type (α,β) of meromorphic function with respect to an entire function, Ganita 70 (2) (2020), 239-252.
[3]	T. Biswas, C. Biswas and R. Biswas, A note on generalized growth analysis of composite entire functions, Poincare J. Anal. Appl. 7 (2) (2020), 277-286. · Zbl 1474.30210
[4]	T. Biswas and C. Biswas, Generalized order (α, β) orientied some growth properties of composite entire functions, Ural Math. J. 6 (2) (2020), 25-37. · Zbl 1462.30052
[5]	T. Biswas, 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
[6]	I. Chyzhykov and N. Semochko, Fast growing entire solutions of linear differential equations, Math. Bull. Shevchenko Sci. Soc. 13 (2016), 68-83. · Zbl 1374.34362
[7]	J. Clunie, The composition of entire and meromorphic functions, Mathematical Essays dedicated to A. J. Macintyre, Ohio University Press (1970), 75-92. · Zbl 0218.30032
[8]	W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964. · Zbl 0115.06203
[9]	X. Shen, J. Tu and H. Y. Xu, 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 pages, http://www.advancesindifferenceequations.com/content/2014/1/200. · Zbl 1417.30022
[10]	O. P. Juneja, G. P. Kapoor and S. K. Bajpai, 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
[11]	I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993. · Zbl 0784.30002
[12]	Q. Lin and C. Dai, On a conjecture of Shah concerning small functions, Kexue Tong bao ( English Ed.) 31 (4) (1986), 220-224. · Zbl 0605.30033
[13]	M. N. Sheremeta, On the growth of a composition of entire functions, Carpathian Math. Publ. 9 (2) (2017), 181-187. · Zbl 1387.30035
[14]	M. N. Sheremeta, 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).
[15]	D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411-414. · Zbl 0109.30104
[16]	G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, New York (NY), USA, 1949.
[17]	L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993. · Zbl 0790.30018