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A NOTE ON THE GROWTH RATES OF COMPOSITE P-ADIC ENTIRE FUNCTIONS

  • Received : 2021.07.12
  • Accepted : 2021.12.09
  • Published : 2022.03.25

Abstract

The main aim of this paper is to study some growth properties of p -adic entire functions on the basis of generalized relative order (𝛼, 𝛽) where 𝛼 and 𝛽 are continuous non-negative functions on (-∞, +∞).

Keywords

Acknowledgement

The authors are thankful to the referees for their many valuable remarks and suggestions which lead to the improvement of the original version of this paper.

References

  1. L. Bernal, Orden relativo de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209-229.
  2. T. Biswas and C. Biswas, Some Aspects of the Theory of p-adic Entire Functions, GlobeEdit, Chisinau-2068, Republic of Moldova Europe, 145 p., 2021.
  3. T. Biswas and C. Biswas, On the Growth Properties of Composite p-adic Entire Functions, Noor Publishing, Chisinau-2068, Republic of Moldova Europe, 133p., 2021.
  4. T. Biswas, Relative (p, q)-φ order oriented some growth properties of p-adic entire functions, J. Fract. Calc. Appl. 11 (2020), no. 1, 161-169.
  5. T. Biswas, C. Biswas, and R. Biswas, A note on generalized growth analysis of composite entire functions, Poincare J. Anal. Appl. 7 (2020), no. 2, 257-266.
  6. T. Biswas and C. Biswas, Generalized (α, β)order based on some growth properties of wronskians, Mat. Stud. 54 (2020), no. 1, 46-55. https://doi.org/10.30970/ms.54.1.46-55
  7. 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 (2019), no. 3, 1950044, 15p., https://doi.org/10.1142/S179355711950044X.
  8. 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. 31 (2018), no. 4, 429-460. https://doi.org/10.14403/JCMS.2018.31.1.429
  9. 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 (2018), no. 4, 160-169. https://doi.org/10.29229/uzmj.2018-4-16
  10. T. Biswas, Relative order and relative type based growth properties of iterated p-adic entire functions, Korean J. Math. 26 (2018), no. 4, 629-663. https://doi.org/10.11568/KJM.2018.26.4.629
  11. 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 (2018), no. 4, 621-659. https://doi.org/10.5831/HMJ.2018.40.4.621
  12. T. Biswas, (p, q)-th order oriented growth measurement of composite p-adic entire functions, Carpathian Math. Publ. 10 (2018), no. 2, 248-272. https://doi.org/10.15330/cmp.10.2.248-272
  13. 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 (2016), no. 4, 280-297. https://doi.org/10.1134/S2070046616040026
  14. K. Boussaf, A. Boutabaa, and A. Escassut, Growth of p-adic entire functions and applications, Houston J. Math. 40 (2014), no. 3, 715-736.
  15. A. Escassut, K. Boussaf, and A. Boutabaa, Order, type and cotype of growth for p-adic entire functions, Dedicated to the memory of Professor Marc Krasner, Sarajevo J. Math. 12 (2016), no. 2-suppl., 429-446.
  16. A. Escassut, Value Distribution in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd., Singapore, 2015.
  17. A. Escassut and J. Ojeda, Exceptional values of p-adic analytic functions and derivative, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 263-269. https://doi.org/10.1080/17476930903394945
  18. 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, 42-138, 2008.
  19. A. Escassut, Analytic Elements in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd., Singapore, 1995.
  20. P.C. Hu and C.C. Yang, Meromorphic Functions over non-Archimedean Fields, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
  21. 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.
  22. K.S. Kedlaya, p-adic differential equations, Cambridge University Press, Cambridge, 2010.
  23. A. Robert, A Course in p-adic analysis, Graduate texts, Springer, New York, 2000.
  24. M.N. Sheremeta, Connection between the growth of the maximum of the modulus of an entire function and the moduli of the coefficients of its power series expansion, Izv. Vyssh. Uchebn. Zaved Mat. 2 (1967), 100-108 (in Russian).