On integral representations of (α,β,γ)-type and (α,β,γ)-weak type of meromorphic function
Bhattacharyya, S., Biswas, T., Biswas, C. (2024). On integral representations of (α,β,γ)-type and (α,β,γ)-weak type of meromorphic function. EKB Journal Management System, 15(1), 1-13. doi: 10.21608/jfca.2023.241241.1042
Sarmila Bhattacharyya; Tanmay Biswas; Chinmay Biswas. "On integral representations of (α,β,γ)-type and (α,β,γ)-weak type of meromorphic function". EKB Journal Management System, 15, 1, 2024, 1-13. doi: 10.21608/jfca.2023.241241.1042
Bhattacharyya, S., Biswas, T., Biswas, C. (2024). 'On integral representations of (α,β,γ)-type and (α,β,γ)-weak type of meromorphic function', EKB Journal Management System, 15(1), pp. 1-13. doi: 10.21608/jfca.2023.241241.1042
Bhattacharyya, S., Biswas, T., Biswas, C. On integral representations of (α,β,γ)-type and (α,β,γ)-weak type of meromorphic function. EKB Journal Management System, 2024; 15(1): 1-13. doi: 10.21608/jfca.2023.241241.1042

On integral representations of (α,β,γ)-type and (α,β,γ)-weak type of meromorphic function

Journal of Fractional Calculus and Applications
Article 7, Volume 15, Issue 1, January 2024, Page 1-13  XML PDF (433.56 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2023.241241.1042
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Authors
Sarmila Bhattacharyya email 1; Tanmay Biswas2; Chinmay Biswas3
1Department of Mathematics, Netaji Mahavidyalaya, P.O.- Arambagh, Dist.-Hooghly, PIN-712601, West Bengal, India
2Rajbari, Rabindrapally, R. N. Tagore Road, P.O. Krishnagar, P.S.- Katwali, Dist-Nadia, PIN- 741101, West Bengal, India.
3Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.-Nadia, PIN-741302, West Bengal, India
Abstract
In complex analysis, order and type are classical growth indicators of entire and meromorphic functions. During the past decades, several authors have made the close investigations on the properties of entire and meromorphic functions in different directions using the concepts of order, the iterated p-order [8, 11], the (p,q)-th order [6, 7], (p,q)-ϕ order [10] and achieved many valuable results. But in [3], Chyzhykov et al. showed that both definitions of iterated p-order and the (p,q)-th order have the disadvantage that they do not cover arbitrary growth (see [3], Example 1.4). They used more general scale, called the ϕ-order (see [3]). On the other hand, Heittokangas et al. [4] have introduced another new concept of ϕ-order of entire and meromorphic functions considering ϕ as subadditive function. Considering all these aspects, Belaïdi et al. [1, 2] have extended the above ideas and have introduced the definitions of (α,β,γ)-order and (α,β,γ)-type of entire and meromorphic functions. In this paper, we establish the integral representations of (α,β,γ)-type and (α,β,γ)-weak type of a meromorphic function. We also investigate their equivalence relation under some certain conditions.
Keywords
Meromorphic function; (α,β,γ)-type; integral representation
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