The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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SOME RESULTS ON (p, q)-TH RELATIVE RITT ORDER AND (p, q)-TH RELATIVE RITT TYPE OF ENTIRE FUNCTIONS REPRESENTED BY VECTOR VALUED DIRICHLET SERIES

  • Received : 2018.03.27
  • Accepted : 2018.11.24
  • Published : 2018.11.30
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Abstract

In this paper we wish to establish some basic properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.

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References

  1. L. Bernal: Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones enteras con ndice exponencial nito, Doctoral Dissertation, University of Seville, Spain, 1984.
  2. L. Bernal: Orden relativo de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209-229.
  3. T. Biswas: On some bounds involving (p,q)-relative Ritt type and (p,q)-relative Ritt weak type of entire functions represented by vector valued Dirichlet series. An. Univ. Oradea, fasc. Mat. Tom XXV(2) (2018), 85-97.
  4. T. Biswas: An extensive study on sum and product theorems of relative (p,q) th order and relative (p,q) th type of meromorphic functions with respect to entire functions. Electron. J. Math. Analysis Appl. 7 (2019), no. 1, 33-64.
  5. S.K. Datta, T. Biswas & P. Das: On relative Ritt type and relative Ritt weak type of entire functions represented by vector valued Dirichlet series. Journal of Calcutta Mathematics Society 11 (2015), no. 2, 67-74.
  6. S.K. Datta & T. Biswas: A few results on relative Ritt type and relative Ritt weak type of entire functions represented by Vector valued Dirichlet series. Poincare J. Anal. Appl. (2016), no. 2 , 49-69.
  7. S.K. Datta & T. Biswas: (p, q)-th relative Ritt order of entire functions in the form of vector valued Dirichlet series. An. Univ. Oradea, fasc. Mat. Tom XXV(1) (2018), 153-162.
  8. O.P. Juneja, K. Nandan & G.P. Kapoor: On the (p, q)-order and lower (p, q)-order of an entire Dirichlet series. Tamkang J. Math. 9 (1978), 47-63.
  9. Q.I. Rahaman: The Ritt order of the derivative of an entire function. Ann. Polon. Math. 17 (1965), 137-140. https://doi.org/10.4064/ap-17-2-137-140
  10. C.T. Rajagopal & A.R. Reddy: A note on entire functions represented by Dirichlet series. Ann. Polon. Math. 17 (1965), 199-208. https://doi.org/10.4064/ap-17-2-199-208
  11. J.F. Ritt: On certain points in the theory of Dirichlet series. Amer. J. Math. 50 (1928), 73-86. https://doi.org/10.2307/2370849
  12. G.S. Srivastava: A note on relative type of entire functions represented by vector valued Dirichlet series J. Class. Anal. 2 (2013), no. 1, 61-72.
  13. G.S. Srivastava & A. Sharma: On generalized order and generalized type of vector valued Dirichlet series of slow growth. Int. J. Math. Archive 2 (2011), no. 12, 2652-2659.
  14. B.L. Srivastava: A study of spaces of certain classes of vector valued Dirichlet series. Thesis, I. I. T., Kanpur, (1983).
  15. R.P. Srivastav & R.K. Ghosh: On entire functions represented by Dirichlet series. Ann. Polon. Math. 13 (1963), 93-100. https://doi.org/10.4064/ap-13-1-93-100