GENERALIZED ORDER \((\alpha ,\beta)\) ORIENTED SOME GROWTH PROPERTIES OF COMPOSITE ENTIRE FUNCTIONS

Tanmay Biswas     (Rajbari, Rabindrapally, R.N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India)
Chinmay Biswas     (Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.-Nadia, PIN-741302, West Bengal, India)

Abstract


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, Composition, Generalized order \((\alpha,\beta )\), Generalized lower order \((\alpha ,\beta )\).

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References


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., 2018. Vol. 13, No. 2. P. 107–122. DOI: 10.7153/jca-2018-13-07

Biswas T., Biswas C., Biswas R. A note on generalized growth analysis of composite entire functions. Poincare J. Anal. Appl., 2020. Vol. 7, No. 2. P. 277–286.

Chyzhykov I., Semochko N. Fast growing entire solutions of linear differential equations. Math. Bull. Shevchenko Sci. Soc., 2016. Vol. 13. P. 68–83. http://journals.iapmm.lviv.ua/ojs/index.php/MBSSS/article/viewFile/2107/2501

Clunie J. The composition of entire and meromorphic functions. In: Mathematical Essays dedicated to A.J. Macintyre. Hari Shankar (ed.) Ohio: Ohio University Press, 1970. P. 75–92.

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., 1976. Vol. 282. P. 53–67. DOI: 10.1515/crll.1976.282.53

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. Vol. 2014, No. 1. Art. no. 200. 14 p. DOI: 10.1186/1687-1847-2014-200

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. Vol. 2. P. 100–108. (in Russian)

Sato D. On the rate of growth of entire functions of fast growth. Bull. Amer. Math. Soc., 1963. Vol. 69, No. 3. P. 411–414. https://projecteuclid.org/euclid.bams/1183525273

Singh A.P. On maximum term of composition of entire functions. Proc. Nat. Acad. Sci. India Sect. A, 1989. Vol. 59, Part I. P. 103-115.

Singh A.P., Baloria M.S. On the maximum modulus and maximum term of composition of entire functions. Indian J. Pure Appl. Math. , 1991. Vol. 22, No. 12. P. 989–996. https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a1f_989.pdf

Valiron G. Lectures on the General Theory of Integral Functions. NY: Chelsea Publishing Company, 1949. 234 p.

Yang L. Value Distribution Theory. Berlin, Heidelberg: Springer-Verlag, 1993. DOI: 10.1007/978-3-662-02915-2




DOI: http://dx.doi.org/10.15826/umj.2020.2.003

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