Central index oriented growth analysis of composite entire functions from the view point of (α,β,γ)-order

Document Type : Regular research papers


1 Research Scientist, Rajbari, Rabindrapally, R. N. Tagore Road P.O. Krishnagar, P.S.-Katwali, Dist-Nadia, PIN- 741101, West Bengal, India

2 Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India

3 Department of Mathematics, Jangipur College, P.O.-Jangipur, Dist.-Murshidabad, PIN-742213, West Bengal, India


Complex analysis is a very important branch of Mathematics and lot of works has been done in this field. One of the important part is growth analysis of entire and meromorphic functions. The ratio $\frac{M_{f}(r)}{M_{g}(r)}$ is called the growth of the entire function $f$ with respect to entire function $g$ in terms of maximum modulus functions. Order and type are classical growth indicators. Definitions of order and type of entire and meromorphic functions have been extended several times. Recently, Bela\"{\i}di et al. [1] have extended the previous ideas and have introduced the definitions of $(\alpha ,\beta ,\gamma )$-order of entire and meromorphic functions. The generalized definitions of order of entire function are obtained by some researchers in terms of central index (see [2, 3]). In this paper, we have discussed on central index oriented some growth properties of composite entire functions on the basis of their $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-lower order, and have generalized some previous works in this line.


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