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RELATIVE ORDER AND RELATIVE TYPE BASED GROWTH PROPERTIES OF ITERATED P ADIC ENTIRE FUNCTIONS

  • Received : 2018.07.14
  • Accepted : 2018.11.19
  • Published : 2018.12.30

Abstract

Let us suppose that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and $\mathcal{A}$ (${\mathbb{K}}$) be the ${\mathbb{K}}$-algebra of entire functions on K. The main aim of this paper is to study some newly developed results related to the growth rates of iterated p-adic entire functions on the basis of their relative orders, relative type and relative weak type.

Keywords

References

  1. L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209-229.
  2. J. P. Bezivin, K. Boussaf and A. Escassut, Zeros of the derivative of a p-adicmeromorphic function, Bulletin des Sciences Math ematiques 136 (8) (2012), 839-847. https://doi.org/10.1016/j.bulsci.2012.07.003
  3. J. P. Bezivin, K. Boussaf and A. Escassut, Some new and old results on zeros of the derivative of a p-adic meromorphic function, Contemp. Math., Amer. Math. Soc., 596 (2013), 23-30.
  4. K. Boussaf, A. Escassut and J. Ojeda, Primitives of p-adic meromorphic functions, Contemp. Math. 551 (2011), 51-56.
  5. K. Boussaf, A. Boutabaa and A. Escassut, Growth of p-adic entire functions and applications, Houston J. Math. 40 (3) (2014), 715-736.
  6. K. Boussaf, A. Escassut and J. Ojeda, Growth of complex and p-adic meromor- phic functions and branched small functions, Bull. Belg. Math. Soc. - Simon Stevin, (2016).
  7. K. Boussaf, A. Boutabaa and A. Escassut, Order, Type and Cotype of Growth for p-Adic Entire Functions: A Survey with Additional Properties, p-Adic Numbers Ultrametric Anal. Appl. 8 (4) (2016), 280-297. https://doi.org/10.1134/S2070046616040026
  8. A. Boutabaa, Theorie de Nevanlinna p-adique, Manuscripta Math. 67 (1990), 251-269. https://doi.org/10.1007/BF02568432
  9. T., Biswas, Some growth properties of composite p-adic entire functions on the basis of their relative order and relative lower order, Asian-Eur. J. Math. Accepted for publication (2018), https://doi.org/10.1142/S179355711950044X.
  10. T. Biswas, Some growth aspects of composite p-adic entire functions in the light of their (p, q)-th relative order and (p, q)-th relative type, J. Chungcheong Math. Soc. 3 (4) (2018), 429-460.
  11. A. Escassut, K. Boussaf and A. Boutabaa, Order, type and cotype of growth for p-adic entire functions, Sarajevo J. Math. 2 (25) (2016), 429-446.
  12. A. Escassut, Analytic Elements in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd. Singapore, (1995).
  13. A. Escassut, p-adic Value Distribution, Some Topics on Value Distribution and Differentability in Complex and P-adic Analysis, p. 42-138. Math. Monogr., Series 11. Science Press.(Beijing 2008).
  14. A. Escassut, Value Distribution in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd. Singapore, (2015).
  15. A. Escassut and J. Ojeda, Exceptional values of p-adic analytic functions and derivative, Complex Var. Elliptic Equ., 56 (1-4) (2011), 263-269. https://doi.org/10.1080/17476930903394945
  16. A. Escassut and J. Ojeda, Branched values and quasi-exceptional values for p-adic mermorphic functions, Houston J. Math. 39 (3) (2013), 781-795.
  17. A. Escassut and J. Ojeda, The p-adic Hayman conjecture when n = 2, Complex Var. Elliptic Equ. 59 (10) (2014), 1452-1455.
  18. P. C. Hu and C. C. Yang, Meromorphic Functions over non-Archimedean Fields, Kluwer Academic Publishers, (2000).
  19. B. K. Lahiri and D. Banerjee, Relative fix points of entire functions, J. India Acad. Math. 19 (1) (1997), 87-97.
  20. A. Robert, A Course in P-Adic Analysis, Graduate texts. Springer (2000).
  21. J. Ojeda, On Hayman's Conjecture over a p-adic field, Taiwanese J. Math., 12 (9) (2008), 2295-2313. https://doi.org/10.11650/twjm/1500405180

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  1. RELATIVE (p, q) - 𝜑 ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS vol.29, pp.2, 2021, https://doi.org/10.11568/kjm.2021.29.2.361