Geodesic
Generalized order $(\alpha ,\beta)$ oriented some growth properties of composite entire functions
Ural mathematical journal, Tome 6 (2020) no. 2, pp. 25-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we establish some results relating to the growths of composition of two entire 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 on $(-\infty ,+\infty )$.
Keywords: entire function, growth, generalized order $(\alpha,\beta )$, generalized lower order $(\alpha,\beta )$.
Mots-clés : composition 
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     title = {Generalized order $(\alpha ,\beta)$ oriented some growth properties of composite entire functions},
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     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a2/}
}
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Tanmay Biswas; Chinmay Biswas. Generalized order $(\alpha ,\beta)$ oriented some growth properties of composite entire functions. Ural mathematical journal, Tome 6 (2020) no. 2, pp. 25-37. http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a2/

[1] Biswas T., “On some inequalities concerning relative $(p,q)-\varphi $ type and relative $(p,q)-\varphi $ weak type of entire or meromorphic functions with respect to an entire function”, J. Class. Anal., 13:2 (2018), 107–122 | DOI | MR | Zbl

[2] Biswas T., Biswas C., Biswas R., “A note on generalized growth analysis of composite entire functions”, Poincare J. Anal. Appl., 7:2 (2020), 277–286 | MR

[3] Chyzhykov I., Semochko N., “Fast growing entire solutions of linear differential equations”, Math. Bull. Shevchenko Sci. Soc., 13 (2016), 68–83 http://journals.iapmm.lviv.ua/ojs/index.php/MBSSS/article/viewFile/2107/2501 | Zbl

[4] Clunie J., “The composition of entire and meromorphic functions”, Mathematical Essays dedicated to A.J. Macintyre, ed. Hari Shankar, Ohio University Press, Ohio, 1970, 75–92 | MR

[5] Juneja O. P., Kapoor G. P., 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 | DOI | MR | Zbl

[6] Shen X., Tu J., Xu H. Y., “Complex oscillation of a second-order linear differential equation with entire coefficients of $[p,q]-\varphi$ order”, Adv. Differ. Equ., 2014:1 (2014), 200, 14 pp. | DOI | MR | Zbl

[7] 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., 1967, no. 2, 100–108 (in Russian) | MR

[8] Sato D., “On the rate of growth of entire functions of fast Growth”, Bull. Amer. Math. Soc., 69:3 (1963), 411–414 https://projecteuclid.org/euclid.bams/1183525273 | DOI | MR | Zbl

[9] Singh A. P., “On maximum term of composition of entire functions”, Proc. Nat. Acad. Sci. India Sect. A, 59, Part I (1989), 103-115 | MR | Zbl

[10] Singh A. P., Baloria M. S., “On the maximum modulus and maximum term of composition of entire functions”, Indian J. Pure Appl. Math., 22:12 (1991), 989–996 https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a1f_989.pdf | MR | Zbl

[11] Valiron G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, NY, 1949, 234 pp. | MR

[12] Yang L., Value Distribution Theory, Berlin–Heidelberg, 1993 | DOI | MR