• 호남수학학술지
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• 제44권1호
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• pp.52-61
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• 2022

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 (-∞, +∞).

• 충청수학회지
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• 제31권4호
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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.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.715-723
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• 2021

In this paper we wish to introduce the concept of generalized relative index-pair (𝛼, 𝛽) 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.

• Korean Journal of Mathematics
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• 제26권4호
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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.

• Korean Journal of Mathematics
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• 제29권2호
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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.

• 호남수학학술지
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• 제40권4호
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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.