Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME GROWTH ESTIMATIONS BASED ON (p, q)-𝜑 RELATIVE GOL'DBERG TYPE AND (p, q)-𝜑 RELATIVE GOL'DBERG WEAK TYPE OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

  • Received : 2020.03.05
  • Accepted : 2020.07.29
  • Published : 2020.09.30
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Abstract

In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

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References

  1. D. Banerjee and S. Sarkar, (p, q)th Gol'dberg order of entire functions of several variables, Int. J. Math. Sci. Eng. Appl. 11 (2017) (3), 185-201.
  2. T. Biswas, Some results relating to (p, q)-th relative Gol'dberg order and (p, q)-relative Gol'dberg type of entire functions of several variables, J. Fract. Calc. Appl. 10 (2019) (2), 249-272.
  3. T. Biswas, Sum and product theorems relating to relative (p, q)-th Gol'dberg order, relative (p, q)-th Gol'dberg type and relative (p, q)-th Gol'dberg weak type of entire functions of several variables, J. Interdiscip. Math. 22 (2019) (1), 53-63. https://doi.org/10.1080/09720502.2018.1564581
  4. T. Biswas and R. Biswas, Sum and product theorems relating to (p, q)-${\varphi}$ relative Gol'dberg order and (p, q)-${\varphi}$ relative Gol'dberg lower order of entire functions of several variables, Uzbek Math. J. 2019 (1), 143-155. https://doi.org/10.29229/uzmj.2019-4-15
  5. T. Biswas and R. Biswas, Some growth properties of entire functions of several complex variables on the basis of their (p, q)-${\varphi}$ relative Gol'dberg order and (p, q)-${\varphi}$ relative Gol'dberg lower order, Electron. J. Math. Anal. Appl. 8 (2020) (1), 229-236.
  6. T. Biswas and R. Biswas, On some (p, q)-${\varphi}$ relative Gol'dberg type and (p, q)-${\varphi}$ relative Gol'dberg weak type based growth properties of entire functions of several complex variables, Ital. J. Pure Appl. Math. 44 (2020), 403-414.
  7. S. K. Datta and A. R. Maji, Study of Growth properties on the basis of generalised Gol'dberg order of composite entire functions of several complex variables, Int. J. Math. Sci. Eng. Appl. 5 (2011) (5), 297-311.
  8. S.K. Datta and A.R. Maji, Some study of the comparative growth rates on the basis of generalised relative Gol'dberg order of composite entire functions of several complex variables, Int. J. Math. Sci. Eng. Appl. 5 (2011) (5), 335-344.
  9. S.K. Datta and A.R. Maji, Some study of the comparative growth properties on the basis of relative Gol'dberg order of composite entire functions of several complex variables, Int. J. Contemp. Math. Sci. 6 (2011) (42), 2075-2082.
  10. B. A. Fuks, Introduction to the theory of analytic functions of several complex variables, American Mathematical Society, Providence, R. I., 1963.
  11. A. A. Gol'dberg, Elementary remarks on the formulas defining order and type of functions of several variables. (Russian) Akad. Nauk Armjan. SSR Dokl. 29 (1959), 145-151.
  12. B. C. Mondal and C. Roy, Relative Gol'dberg order of an entire function of several variables, Bull Calcutta Math. Soc. 102 (2010) (4), 371-380.
  13. C. Roy, Some properties of entire functions in one and several complex vaiables, Ph.D. Thesis (2010), University of Calcutta.
  14. X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q]-${\varphi}$ order, Adv. Difference Equ. 2014,2014: 200, 14 pages, http://www.advancesindifferenceequations.com/content/2014/1/200. https://doi.org/10.1186/1687-1847-2014-200