Some growth properties of analytic functions relating to (α,β,γ)-Nevanlinna order and (α,β,γ)-Nevanlinna type in the unit disc
Biswas, T., Biswas, C., Bhattacharyya, S., Biswas, S. (2024). Some growth properties of analytic functions relating to (α,β,γ)-Nevanlinna order and (α,β,γ)-Nevanlinna type in the unit disc. EKB Journal Management System, 12(2), 1-10. doi: 10.21608/ejmaa.2024.290032.1202
Tanmay Biswas; Chinmay Biswas; Sarmila Bhattacharyya; Susmita Biswas. "Some growth properties of analytic functions relating to (α,β,γ)-Nevanlinna order and (α,β,γ)-Nevanlinna type in the unit disc". EKB Journal Management System, 12, 2, 2024, 1-10. doi: 10.21608/ejmaa.2024.290032.1202
Biswas, T., Biswas, C., Bhattacharyya, S., Biswas, S. (2024). 'Some growth properties of analytic functions relating to (α,β,γ)-Nevanlinna order and (α,β,γ)-Nevanlinna type in the unit disc', EKB Journal Management System, 12(2), pp. 1-10. doi: 10.21608/ejmaa.2024.290032.1202
Biswas, T., Biswas, C., Bhattacharyya, S., Biswas, S. Some growth properties of analytic functions relating to (α,β,γ)-Nevanlinna order and (α,β,γ)-Nevanlinna type in the unit disc. EKB Journal Management System, 2024; 12(2): 1-10. doi: 10.21608/ejmaa.2024.290032.1202

Some growth properties of analytic functions relating to (α,β,γ)-Nevanlinna order and (α,β,γ)-Nevanlinna type in the unit disc

Electronic Journal of Mathematical Analysis and Applications
Volume 12, Issue 2, 2024, Page 1-10  XML PDF (513.39 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2024.290032.1202
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Authors
Tanmay Biswasorcid 1; Chinmay Biswas email orcid 2; Sarmila Bhattacharyya3; Susmita Biswas4
1Rajbari, Rabindrapally, R. N. Tagore Road, P.O.-Krishnagar, P.S.-Katwali, Dist.-Nadia, PIN- 741101, West Bengal, India.
2Department of Mathematics, Nabadwip Vidyasagar College, P.O.-Nabadwip, P.S.-Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India.
3Department of Mathematics, Netaji Mahavidyalaya, P.O.- Arambagh, Dist.-Hooghly, PIN-712601, West Bengal, India.
4Department of Cyber Science & Technology, Brainware University, 398 Ramkrishnapur Road, Barasat, Kolkata-7000125, India
Abstract
Growth analysis of analytic functions is very important part of research in
the field of complex analysis and many researchers are involved in this area
during past decades. Collecting ideas from Heittokangas et al. (Meromorphic
functions of finite $\varphi $-order and linear q-difference equations, J.
Difference Equ. Appl., 27 (9) (2021), 1280-1309) and Bela\"{\i}di et
al. (Study of complex oscillation of solutions of a second order linear
differential equation with entire coefficients of $(\alpha ,\beta ,\gamma )$%
-order, WSEAS Trans. Math., 21 (2022), 361-370), here in this paper,
we have defined the $(\alpha ,\beta ,\gamma )$-Nevanlinna order and\ $%
(\alpha ,\beta ,\gamma )$-Nevanlinna type of an analytic function $f$ in the
unit disc $U$. We have also established some growth properties of the
composition of two analytic functions in the unit disc on the basis of their
$(\alpha ,\beta ,\gamma )$-Nevanlinna order, $(\alpha ,\beta ,\gamma )$%
-Nevanlinna lower order, $(\alpha ,\beta ,\gamma )$-Nevanlinna type and $%
(\alpha ,\beta ,\gamma )$-Nevanlinna weak type as compared to the growth of
their corresponding left and right factors, where $\alpha ,\beta ,\gamma $
are continuous non-negative functions defined on $(-\infty ,+\infty )$.
Keywords
Analytic function in unit disc; growth; (α β γ)-Nevanlinna order; (α β γ)-Nevanlinna type; (α β γ)-Nevanlinna weak type
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