Relative p-th Order of Entire Functions of Several Complex Variables

Ratan Kumar Dutta; Nintu Mandal

doi:https://doi.org/10.14445/22315373/IJMTT-V46P534

International Journal of Mathematics Trends and Technology

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Volume 46 | Number 4 | Year 2017 | Article Id. IJMTT-V46P534 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P534

Relative p-th Order of Entire Functions of Several Complex Variables

Ratan Kumar Dutta, Nintu Mandal

Abstract

In this paper we introduce the idea of relative p-th order of entire functions of several complex variables. After proving some basic results, we observe that the relative p-th order of a transcendental entire function with respect to an entire function is the same as that of its partial derivatives. Further we study the equality of relative p-th order of two entire functions when they are asymptotically equivalent.

Keywords

Entire functions, polydisc, relative order, relative p-th order, several complex variables.

References

[1] AK. Agarwal, On the properties of an entire function of two complex variables, Canadian Journal of Mathematics, 20 (1968), pp. 51-57.
[2] D. Banerjee and R. K. Dutta, Relative order of entire functions of two complex variables, International J. of Math. Sci. & Engg. Appls., 1(1) (2007), pp. 141-154.
[3] L. Bernal, Orden relative de crecimiento de funcionesenteras, Collect. Math. 39 (1988), pp. 209-229.
[4] R. K. Dutta, Relative order of entire functions of several complex variables, Mat. Vesnik, 65, 2(2013), pp. 222-233.
[5] R. K. Dutta and N. Mandal, Relative p-th order of entire functions of two complex variables,Int. J. Eng. Tech. Research 3(10) October 2015, pp. 164-168.
[6] B. A. Fuks, Theory of analytic functions of several complex variables, Moscow, 1963.
[7] S. Halvarsson, Growth properties of entire functions depending on a parameter, AnnalesPoloniciMathematici, 14(1) (1996), pp. 71-96.
[8] C. O. Kiselman, Order and type as measures of growth for convex or entire functions, Proc. Lond. Math.Soc., 66(3) (1993), pp. 152-186.
[9] C. O. Kiselman, Plurisubharmonic functions and potential theory in several complex variables, a contribution to the book project, Development of Mathematics 1950-2000, edited by jean-Paul Pier.
[10] B. K. Lahiri and Dibyendu Banerjee, Generalized relative order of entire functions, Proc. Nat. Acad. Sci. India, 72(A), IV (2002), pp. 351-371.
[11] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), pp. 411-414.

Citation :

Ratan Kumar Dutta, Nintu Mandal, "Relative p-th Order of Entire Functions of Several Complex Variables," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 4, pp. 235-241, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P534