Korean J. Math.  Vol 29, No 2 (2021)  pp.361-370
DOI: https://doi.org/10.11568/kjm.2021.29.2.361

Relative $(p,q)-\varphi$ order based some growth analysis of composite $p$-adic entire functions

Tanmay Biswas, Chinmay Biswas

Abstract


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


Keywords


$p$-adic entire function, growth, composition, relative $(p,q)-\varphi $ order, relative $(p,q)-\varphi $ lower order.

Subject classification

12J25, 30D35, 30G06, 46S10

Sponsor(s)



Full Text:

PDF

References


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

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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)

(Google Scholar)

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. (Google Scholar)

(Google Scholar)

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

(Google Scholar)

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

(Google Scholar)

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)

(Google Scholar)

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

(Google Scholar)

P. C. Hu and C. C. Yang, Meromorphic Functions over non-Archimedean Fields, Kluwer Aca- demic Publishers, (publ. city), 2000. (Google Scholar)

(Google Scholar)

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)

(Google Scholar)

A. Robert, A Course in p-adic analysis, Graduate texts, Springer (publ. city), 2000. (Google Scholar)

(Google Scholar)

X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equa- tion with entire coefficients of [p,q]-φ order, Adv. Difference Equ, 2014:200 (2014), 14 p., http://www.advancesindifferenceequations.com/content/2014/1/200. (Google Scholar)

(Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr