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RELATIVE (p, q) - πœ‘ ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS

Chinmay Biswas|Tanmay Biswas
κ°•μ›κ²½κΈ°μˆ˜ν•™νšŒ (The Kangweon-Kyungki Mathematical Society)|2021.06|ν•œκ΅­μˆ˜ν•™λ…Όλ¬Έμ§‘ (Korean Journal of Mathematics)|제29ꢌ 제2호|pp. 361-370

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growthcompositionrelative (pp-adic entire functionq) - Ο† orderq) - Ο† lower order
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초둝

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 |Β·|(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)-πœ‘ order where p, q are any two positive integers and πœ‘ (r) : [0, +∞) β†’ (0, +∞) is a non-decreasing unbounded function of r.

Abstract

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 |Β·|(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)-πœ‘ order where p, q are any two positive integers and πœ‘ (r) : [0, +∞) β†’ (0, +∞) is a non-decreasing unbounded function of r.

μ°Έκ³ λ¬Έν—Œ (19)

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Relative order and relative type based growth properties of iterated $p$ adic entire functionsTanmay Biswasκ°•μ›κ²½κΈ°μˆ˜ν•™νšŒ Β· ν•œκ΅­μˆ˜ν•™λ…Όλ¬Έμ§‘2018 Β· 제26ꢌ 제4호Some remarks on the growth of composite $p$-adic entire functionChinmay Biswas, Tanmay Biswasκ°•μ›κ²½κΈ°μˆ˜ν•™νšŒ Β· ν•œκ΅­μˆ˜ν•™λ…Όλ¬Έμ§‘2021 Β· 제29ꢌ 제4호MEASURES OF COMPARATIVE GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH TYPE AND RELATIVE (p, q)-TH WEAK TYPETanmay Biswasν•œκ΅­μˆ˜ν•™κ΅μœ‘ν•™νšŒ Β· μ΄λ‘ μˆ˜ν•™κ³Ό κ΅μ§μˆ˜ν•™2019 Β· 제26ꢌ 제1호Growth analysis of composite entire functions from the view point of relative $(p,q)$-th orderTanmay Biswasκ°•μ›κ²½κΈ°μˆ˜ν•™νšŒ Β· ν•œκ΅­μˆ˜ν•™λ…Όλ¬Έμ§‘2018 Β· 제26ꢌ 제3호On some growth analysis of composite entire and meromorphic functions from the view point of their relative $(p,q)$-th type and relative $(p,q)$-th weak typeTanmay Biswasκ°•μ›κ²½κΈ°μˆ˜ν•™νšŒ Β· ν•œκ΅­μˆ˜ν•™λ…Όλ¬Έμ§‘2018 Β· 제26ꢌ 제1호Few Results in connection with Sum and Product Theorems of Relative (p, q)-Ο† order, relative (p, q)-Ο† Type and Relative (p, q)-Ο† Weak Type of Meromorphic Functions with respect to Entire FunctionsTanmay Biswasν•œκ΅­μˆ˜ν•™κ΅μœ‘ν•™νšŒ Β· μ΄λ‘ μˆ˜ν•™κ³Ό κ΅μ§μˆ˜ν•™2019 Β· 제26ꢌ 제4호

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