Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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RELATIVE (p, q) - 𝜑 ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS

  • Received : 2021.02.16
  • Accepted : 2021.04.15
  • Published : 2021.06.30
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Abstract

Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

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Acknowledgement

The authors are very much grateful to the reviewer for his/her valuable suggestions to bring the paper in its present form.

References

  1. L. Bernal, Orden relativo de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209-229.
  2. T. Biswas, Relative (p, q)-φ order oriented some growth properties of p-adic entire functions, J. Fract. Calc. Appl., 11 (1) (2020), 161-169.
  3. 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., 12 (3) (2019), 1950044, 15p., https://doi.org/10.1142/S179355711950044X.
  4. T. Biswas, Some growth aspects of composite p-adicentire functions in the light of their (p, q)-th relative order and (p, q)-th relative type, J. Chungcheong Math. Soc., 31 (4) (2018), 429-460. https://doi.org/10.14403/JCMS.2018.31.1.429
  5. T. Biswas, On some growth analysis of p-adic entire functions on the basis of their (p, q)-th relative order and (p, q)-th relative lower order, Uzbek Math. J., 2018 (4) (2018), 160-169. https://doi.org/10.29229/uzmj.2018-4-16
  6. T. Biswas, Relative order and relative type based growth properties of iterated p-adic entire functions, Korean J. Math., 26 (4) (2018), 629-663. https://doi.org/10.11568/KJM.2018.26.4.629
  7. T. Biswas, A note on (p, q)-th relative order and (p, q)-th relative type of p-adic entire functions, Honam Math. J., 40 (4) (2018), 621-659. https://doi.org/10.5831/HMJ.2018.40.4.621
  8. T. Biswas,(p, q)-th order oriented growth measurement of composite p-adic entire functions, Carpathian Math. Publ., 10 (2) (2018), 248-272. https://doi.org/10.15330/cmp.10.2.248-272
  9. 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
  10. K. Boussaf, A. Boutabaa and A. Escassut, Growth of p-adic entire functions and applications, Houston J. Math., 40 (3) (2014), 715-736.
  11. A. Escassut, K. Boussaf and A. Boutabaa, Order, type and cotype of growth for p-adic entire functions, Sarajevo J. Math., Dedicated to the memory of Professor Marc Krasner, 12(25) (2) (2016), 429-446, suppl.
  12. A. Escassut, Value Distribution in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd., Singapore, 2015.
  13. 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
  14. A. Escassut,p-adic Value Distribution. Some Topics on Value Distribution and Differentability in Complex and P-adic Analysis, Math. Monogr., Series 11, Science Press, Beijing, (2008), 42-138.
  15. A. Escassut, Analytic Elements in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd. Singapore, 1995.
  16. P. C. Hu and C. C. Yang, Meromorphic Functions over non-Archimedean Fields, Kluwer Academic Publishers, (publ. city), 2000.
  17. O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., 282 (1976), 53-67.
  18. A. Robert, A Course in p-adic analysis, Graduate texts, Springer (publ. city), 2000.
  19. X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q]-φ order, Adv. Difference Equ, 2014:200 (2014), 14 p., http://www.advancesindifferenceequations.com/content/2014/1/200.