Relative (α,β,γ)-order of meromorphic function with respect to entire function | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 13, Issue 1, 2025, Pages 1-10 PDF (235.88 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2025.326940.1277 | ||
| Authors | ||
| Chinmay Biswas* 1; Bablu Chandra Das2 | ||
| 1Department of Mathematics, Nabadwip Vidyasagar College, P.O.-Nabadwip, P.S.-Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India. | ||
| 2Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India | ||
| Abstract | ||
| The growth investigation of meromorphic function has usually been done through the Nevanlinna's characteristic function comparing with the exponential function. Order and type are the classical growth indicators which are generalized by several authors during the past decades. Belaïdi et al. [3] have introduced the concepts of (α,β,γ)-order and (α,β,γ)-lower order of a meromorphic function taking α∈L₁-class, β∈L₂-class, γ∈L₃-class. But if one is paying attention to evaluate the growth rates of any meromorphic function with respect to a entire function, the notions of relative growth indicators (see e.g. [1, 2]) will come. In order to make some progresses in the study of growth analysis of meromorphic functions, here in this paper, we have introduced the definitions of the relative (α,β,γ)-order and relative (α,β,γ)-lower order of a meromorphic function with respect to an entire function as well as their integral representations. We have also investigated some growth properties of meromorphic functions on the basis of relative (α,β,γ)-order and relative (α,β,γ)-lower order as compared to the growth of their corresponding left and right factors. | ||
| Keywords | ||
| Meromorphic function; relative (α β γ)-order; relative (α β γ)-lower order; integral representation | ||
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