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RELATIVE (p, q) - 𝜑 ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS

  • Received : 2021.02.16
  • Accepted : 2021.04.15
  • Published : 2021.06.30

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 |·|(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.

Keywords

Acknowledgement

The authors are very much grateful to the reviewer for his/her valuable suggestions to bring the paper in its present form.

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