Document Type: Research Paper

Authors

1 Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.

2 Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.

Abstract

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Keywords

Main Subjects

[1] A.K. Agarwal, On the properties of entire function of two complex variables, Canadian Journal of Mathematics, 20 (1968) 51-57.

[2] L. Bernal, Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones enteras con ndice exponencial nito, Doctoral Dissertation, University of Seville, Spain, 1984.

[3] L. Bernal, Orden relativo de crecimiento de funciones enteras, Collect. Math., 39 (1988) 209-229.

[4] D. Banerjee and R. K. Dutta, Relative order of entire functions of two complex variables, International J. of Math. Sci. & Engg. Appls. (IJMSEA), 1(1) (2007) 141-154.

[5] A.B. Fuks, Theory of analytic functions of several complex variables, Moscow, 1963.

[6] S. Halvarsson, Growth properties of entire functions depending on a parameter, Annales Polonici Mathematici, 14(1) (1996) 71-96.

[7] O.P. Juneja, G.P. Kapoor, and S.K. Bajpai, On the (p,q)-order and lower $(p,q)$-order of an entire function, J. Reine Angew. Math., 282 (1976) 53-67.

[8] C.O. Kiselman, Order and type as measure of growth for convex or entire functions, Proc. Lond. Math. Soc., 66(3) (1993) 152-186.

[9] C.O. Kiselman, Plurisubharmonic functions and potential theory in several complex variable, a contribution to the book project, Development of Mathematics, 1950-2000, edited by Hean-Paul Pier.

[10] B.K. Lahiri and D. Banerjee, A note on relative order of entire functions, Bull. Cal. Math. Soc., 97(3) (2005) 201-206.

[11] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963) 411-414.

[12] E.C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, 1968.