TY - JOUR
ID - 5313
TI - Entire functions and some of their growth properties on the basis of generalized order (α,β)
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Biswas, Tanmay
AU - Biswas, Chinmay
AU - Saha, Biswajit
AD - Rajbari, Rabindrapally, R. N. Tagore Road P.O. Krishnagar, Dist-Nadia, PIN- 741101, West Bengal, India
AD - Department of Mathematics,Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India
AD - Department of Mathematics, Government General Degree
College Muragachha, Nakashipara, Dist.- Nadia, PIN-741154,West Bengal, India
Y1 - 2021
PY - 2021
VL - 12
IS - 2
SP - 1735
EP - 1747
KW - Entire function
KW - Growth
KW - composition
KW - generalized order $(\alpha, \beta ) $
KW - generalized lower order $(\alpha,\beta )$
DO - 10.22075/ijnaa.2021.22299.2346
N2 - For 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.
UR - https://ijnaa.semnan.ac.ir/article_5313.html
L1 - https://ijnaa.semnan.ac.ir/article_5313_a269705c98c98c6c5301ed8b92b7f7ff.pdf
ER -