Sum and product related theorems of entire function in terms of (α,β,γ)-order | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 1, 2025, Pages 1-6 PDF (181.4 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.317726.1130 | ||
| Authors | ||
| Chinmay Biswas* 1; Bablu Chandra Das1; Sudipta Kumar Pal2 | ||
| 1Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India. | ||
| 2Department of Mathematics, Jangipur College, P.O.-Jangipur, Dist.-Murshidabad, PIN-742213, West Bengal, India. | ||
| Abstract | ||
| Growth analysis of entire and meromorphic function is a very important part in complex analysis. Order is a classical growth indicator of entire and meromorphic functions. During the past several years, many renowned Mathematicians have made the close investigations on the properties of entire and meromorphic functions in different directions using the concepts of order and some extended definitions of order, like iterated $p$-order [7, 8], $(p,q)$-th order [5, 6], $(p,q)$-$\varphi $ order [9], $\varphi $-order [3] etc.\ and they have achieved many valuable results. Heittokangas et al. [4] have introduced another the concept of $\varphi $-order of entire and meromorphic functions considering $\varphi $ as subadditive function. Later, Bela\"{\i}di et al. [1] have extended the above ideas and have introduced the definitions of $(\alpha ,\beta,\gamma )$-order and\ $(\alpha ,\beta ,\gamma )$-lower order of entire and meromorphic functions. In this paper, we investigate some basic properties in connection with sum and product of $(\alpha ,\beta ,\gamma )$-order and\ $(\alpha ,\beta ,\gamma )$-lower order of entire function with respect to another entire function where $\alpha ,\beta ,\gamma $ are continuous non-negative functions defined on $(-\infty ,+\infty )$ with $\alpha \in L_{1}$, $\beta \in L_{2}$, $\gamma \in L_{3}$. | ||
| Keywords | ||
| Growth; Property (A); (α; β; γ)-order | ||
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