• Korean Journal of Mathematics
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• v.26 no.4
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• pp.629-663
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• 2018

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.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.449-472
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• 2015

Let X be a nonempty set and $\mathcal{F}$(X) be the set of nonempty finite subsets of X. The paper deals with the extended metrics ${\tau}:\mathcal{F}(X){\rightarrow}\mathbb{R}$ recently introduced by Peter Balk. Balk's metrics and their restriction to the family of sets A with ${\mid}A{\mid}{\leqslant}n$ make possible to consider "distance functions" with n variables and related them quantities. In particular, we study such type generalized diameters $diam_{{\tau}^n}$ and find conditions under which $B{\mapsto}diam_{{\tau}^n}B$ is a Balk's metric. We prove the necessary and sufficient conditions under which the restriction ${\tau}$ to the set of $A{\in}\mathcal{F}(X)$ with ${\mid}A{\mid}{\leqslant}3$ is a symmetric G-metric. An infinitesimal analog for extended by Balk metrics is constructed.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.429-460
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• 2018

Let us consider that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and ${\mathcal{A}}({\mathbb{K}})$ be the ${\mathbb{K}}-algebra$ of entire functions on ${\mathbb{K}}$. In this paper we introduce the notions of (p, q)-th relative order and (p, q)-th relative type of p adic entire functions where p and q are any two positive integers and then study some growth properties of composite p adic entire functions in the light of their (p, q)-th relative order and (p, q)-th relative type. After that we show that (p, q) th relative order and (p, q)-th relative type are remain unchanged for derivatives under some certain conditions.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.621-659
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• 2018

Let us consider that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and A (${\mathbb{K}}$) be the ${\mathbb{K}}$-algebra of entire functions on ${\mathbb{K}}$. In this paper we introduce the notions of (p, q)-th relative order and (p, q)-th relative type of entire functions on ${\mathbb{K}}$ where p and q are any two positive integers and then study some basic properties of p-adic entire functions on the basis of their (p, q)-th relative order and (p, q)-th relative type.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.361-370
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• 2021

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.