On the growth estimates of entire functions of double complex variables

Year 2017, Volume: 5 Issue: 2, 252 - 272, 30.03.2017

Sanjib Kumar Datta , Tanmay Biswas

https://izlik.org/JA85UZ35YM

Abstract

Recently Datta et al. [6] introduced the idea of relative type and relative weak type of entire functions of two complex variables with respect to another entire function of two complex variables and prove some related growth properties of it. In this paper, further we study some growth properties of entire functions of two complex variables on the basis of their relative types and relative weak types as introduced by Datta et al [6].

Keywords

Entire function of two complex variables , order (lower order) of entire function of two complex variables , relative order (relative lower order) of entire functions of two complex variable

References

• A. K. Agarwal : On the properties of entire function of two complex variables, Canadian Journal of Mathematics, Vol. 20 (1968), pp. 51-57.
• L. Bernal : Crecimiento relativo de funciones enteras. Contribuci´on al estudio de lasfunciones enteras con´ındice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
• L. Bernal : Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp.209-229.
• D. Banerjee and R. K. Datta : Relative order of entire functions of two complex variables, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 1, No. 1 (2007), pp. 141-154
• S. K. Datta, T. Biswas and G. K. Mondal: A note on the relative order of entire functions of two complex variables, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 101, No. 3 (2015), pp. 339-347.
• S. K. Datta, T. Biswas and S. Bhattacharyya: On relative type and weak type of entire functions of two complex variables, Facta Universititatis series: Mathematics and Informatics, Accepted for publication (2016) and to appear.
• A. B. Fuks : Theory of analytic functions of several complex variables, (1963), Moscow.
• S. Halvarsson : Growth properties of entire functions depending on a parameter, Annales Polonici Mathematici, Vol. 14, No.1 (1996), pp. 71-96.
• C. O. Kiselman : Order and type as measure of growth for convex or entire functions, Proc. Lond. Math. Soc., Vol. 66, No.3 (1993), pp. 152-186.
• 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.
• B. K. Lahiri and D. Banerjee : A note on relative order of entire functions, Bull. Cal.Math. Soc. Vol. 97, No. 3 (2005), pp. 201-206.