Korean J. Math. Vol. 29 No. 4 (2021) pp.715-723
DOI: https://doi.org/10.11568/kjm.2021.29.4.715

Some remarks on the growth of composite $p$-adic entire function

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Tanmay Biswas
Chinmay Biswas

Abstract

In this paper we wish to introduce the concept of generalized relative index-pair $(\alpha ,\beta)$ of a $p$-adic entire function with respect to another $p$-adic entire function and then prove some results relating to the growth rates of composition of two $p$-adic entire functions with their corresponding left and right factors.



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References

[1] L. Bernal, Orden relativo de crecimiento de funciones enteras, Collect. Math., 39 (1988), 209– 229. Google Scholar

[2] 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. Google Scholar

[3] 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. Google Scholar

[4] T. Biswas, C. Biswas and R. Biswas, A note on generalized growth analysis of composite entire functions, Poincare J. Anal. Appl., 7 (2) (2020), 257–266. Google Scholar

[5] T. Biswas and C. Biswas, Generalized (α,β) order based on some growth properties of wron- skians, Mat. Stud., 54 (1) (2020), 46–55. Google Scholar

[6] 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. Google Scholar

[7] 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. Google Scholar

[8] 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. Google Scholar

[9] T. Biswas, Relative order and relative type based growth properties of iterated p-adic entire functions, Korean J. Math., 26 (4) (2018), 629–663. Google Scholar

[10] 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. Google Scholar

[11] T. Biswas, (p,q)-th order oriented growth measurement of composite p-adic entire functions, Carpathian Math. Publ., 10 (2) (2018), 248–272. Google Scholar

[12] 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. Google Scholar

[13] K. Boussaf, A. Boutabaa and A. Escassut, Growth of p-adic entire functions and applications, Houston J. Math., 40 (3) (2014), 715–736. Google Scholar

[14] 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, supply. Google Scholar

[15] A. Escassut, Value Distribution in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd., Singapore, 2015. Google Scholar

[16] A. Escassut and J. Ojeda, Exceptional values of p-adic analytic functions and derivative, Com- plex Var. Elliptic Equ., 56 (1-4) (2011), 263–269. Google Scholar

[17] 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. Google Scholar

[18] A. Escassut, Analytic Elements in p-adic Analysis, World Scientific Publishing Co. Pte. Ltd. Singapore, 1995. Google Scholar

[19] P. C. Hu and C. C. Yang, Meromorphic Functions over non-Archimedean Fields, Kluwer Aca- demic Publishers, Dordrecht, The Netherlands, 2000. Google Scholar

[20] O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-type and lower (p,q)-type of an entire function, J. Reine Angew. Math., 290 (1977), 180-190. Google Scholar

[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. Google Scholar

[22] A. Robert, A Course in p-adic analysis, Graduate texts, Springer, New York, 2000. Google Scholar

[23] 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). Google Scholar