Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212220211101Entire functions and some of their growth properties on the basis of generalized order (α,β)17351747531310.22075/ijnaa.2021.22299.2346ENTanmayBiswasRajbari, Rabindrapally, R. N. Tagore Road P.O. Krishnagar, Dist-Nadia, PIN- 741101, West Bengal, IndiaChinmayBiswasDepartment of Mathematics,Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, IndiaBiswajitSahaDepartment of Mathematics, Government General Degree
College Muragachha, Nakashipara, Dist.- Nadia, PIN-741154,West Bengal, IndiaJournal Article20210103For any two entire functions $f$, $g$ defined on finite complex plane $\mathbb{C}$, the ratios $\frac{M_{f\circ g}(r)}{M_{f}(r)}$ and $\frac{M_{f\circ g}(r)}{M_{g}(r)}$ as $r\rightarrow \infty $ are called the growth of composite entire function $f\circ g$ with respect to $f$ and $g$ respectively in terms of their maximum moduli. Several authors have worked about growth properties of functions in different directions. In this paper, we have discussed about the comparative growth properties of $f\circ g$, $f$ and $g,$ and derived some results relating to the generalized order $(\alpha ,\beta )$ after revised the original definition introduced by Sheremeta, where $\alpha ,$ $\beta $ are slowly increasing continuous functions defined on $(-\infty,+\infty )$. Under different conditions, we have found the limiting values of the ratios formed from the left and right factors on the basis of their generalized order $(\alpha ,\beta )$ and generalized lower order $(\alpha,\beta ),$ and also established some inequalities in this regard.https://ijnaa.semnan.ac.ir/article_5313_a269705c98c98c6c5301ed8b92b7f7ff.pdf