Growth Analysis of Composite Entire Functions of Several Complex Variables Based on Relative Order
DOI:
https://doi.org/10.32628/IJSRSET207447Keywords:
Entire functions, Several complex variables, Maximum modulus, comparative growth, relative order L^*-order, ralative L^*-lower order , Maximum term.
Abstract
In this paper we introduce some new results depending on the comparative growth properties of composition of entire function of several complex variables using relative L^*-order, Relative L^*-lower order and L≡L(r_1,r_2,r_3,……..,r_n) is a slowly changing functions. We prove some relation between relative L^*- order and relative L^*- lower order.
References
- A.D. Singh, On maximum term of composite of entire functions, Proc. Nat. Acad. Sci. India., 59(A) (Part I) (1989) (103 - 115).
- A.D. Singh, M.S. Baloria, On maximum modulus and maximum term of composite of entire functions, Indian J.Pure Appl.Math.,22(12) (1991) 1019 – 1026.
- B.A. Fuks, Theory of analytic functions of several complex variables, Moscow,1963.
- C.O. Kiselman, Order and type as measures of growth for convex or entire functions, Proc.Lond.Math.Soc.66(1993),152 – 186.
- C.O. Kiselman, Pluzisubharmonic functions and potential theory in several complex variables a contribution to the book project, Development of Mathematics 1950 – 2000, edited by Jean Panlpier.
- D. Banerjee, R.K. Datta, Relative order of entire functions of two complex variables, International J.Math.Sci.& Engg.Appl.1(2007),141 – 154.
- D. Somasundaram, R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J.Pure Appl.Math.,19(3) (March 1988),284 – 293.
- E.C. Titch marsh, the Theory of functions, 2nd ed. Oxford University Press, Oxford, 1968.
- G. Valiron, Lectures on the General theory of Integral, Chelsea Publishing Company, 1949.
- J. Clunie, The composition of entire and meromorphic functions, Mathematical Essays dedicated to A. J. Macintyre, hio University Press,(1970) 75 – 92.
- L. Bernal, Order relative de. Crecimiento de functions enteras, Collect.Math. 39(1988) 209 – 229.
- R.K. Datta, Relative order of Entire functions of several complex variables, Mathematici Bechik 65,2(2013),222 – 233.
- S. Halvarsson, Growth properties of entire functions depending on a parameter, Anales Polonici Math.14(1996),71 – 96.
- S.K. Dutta, A.R. Maji, Relative order of entire functions in terms of their maximum terms, Int.Journal of Math.Analysis,5(43) (2011) 2119 – 2126.
- S.K. Dutta, T. Biswas, D.C. Pramanik, on the growth analysis relative to Maximum Terms based Relative order of entire functions, International J. of Math. Sci. & Engg. Appls. (IJMSEA),8(V) (September,2014) 231 – 242.
- S.K. Dutta, T. Biswas, D.C. Pramanik, On relative order and maximum term – related comparative growth rates of entire functions, Journal of Tripura Mathematical Society, 14 (2012),60 – 68.
- S.K. Dutta, S. Kar, On the L-Order of meromorphic functions based on relative sharing, International Journal of Pure and Applied Mathematics (IJPAM) ,56(2009) 43 – 47.
- S.K. Dutta, T. Biswas, Growth of entire functions based on relative order, International Journal of Pure and Applied Mathematics (IJPAM) ,51(2009) 49 – 58.
- S.K. Dutta, T. Biswas, R. Biswas, On relative based growth estimates of entire functions , International J. of Math. Sci. & Engg. Appls. (IJMSEA),7(II)(March,2013), 59 – 67.
- S. K. Dutta, T. Biswas, R. Biswas, Comparative growth properties of composite entire functions in the light of their relative order, The mathematics student, 82(1-4) (2013) 209 – 216.
- S.K. Dutta, T. Biswas, and S. Ali, Growth estimates of composite entire functions based on maximum terms using their relative L-order, Advances in Applied Mathematical Analysis, 7(2012),119 – 134.
- S.K. Dutta, T. Biswas, S. Bhattacharyya, Relative orders and slowly changing functions oriented growth analysis of composite entire functions. Int.J.Non linear Anal. Appl.6(2015),No.2,113 – 126.
- S.K. Dutta, T. Biswas, S. Bhattacharyya, Growth Analysis of composite entire functions relative to slowly changing functions oriented relative order and relative type, Journal of Complex Analysis, 2014, Article ID 503719, 8 pages.
- S.K. Singh, G.P. Barker. Slowly changing functions and their applications, Indian J. Math.,19(1977),1 – 6.
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