• Title/Summary/Keyword: relative (p, q)-${\varphi}$ order

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RELATIVE (p, q)-𝜑 ORDER AND RELATIVE (p, q)-𝜑 TYPE ORIENTED GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.243-268
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    • 2019
  • The main aim of this paper is to study some growth properties of composite entire functions on the basis of relative $(p,q)-{\varphi}$ type and relative $(p,q)-{\varphi}$ weak type where p and q are any two positive integers and ${\varphi}(r):[0,+{\infty}){\rightarrow}(0,+{\infty})$ be a non-decreasing unbounded function.

SUM AND PRODUCT THEOREMS OF (p, q)-𝜑 RELATIVE GOL'DBERG TYPE AND (p, q)-𝜑 RELATIVE GOL'DBERG WEAK TYPE OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.28 no.4
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    • pp.819-845
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    • 2020
  • In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

SOME GROWTH ESTIMATIONS BASED ON (p, q)-𝜑 RELATIVE GOL'DBERG TYPE AND (p, q)-𝜑 RELATIVE GOL'DBERG WEAK TYPE OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

  • Biswas, Tanmay;Biswas, Ritam
    • Korean Journal of Mathematics
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    • v.28 no.3
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    • pp.489-507
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    • 2020
  • In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

FEW RESULTS IN CONNECTION WITH SUM AND PRODUCT THEOREMS OF RELATIVE (p, q)-𝜑 ORDER, RELATIVE (p, q)-𝜑 TYPE AND RELATIVE (p, q)-𝜑 WEAK TYPE OF MEROMORPHIC FUNCTIONS WITH RESPECT TO ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • The Pure and Applied Mathematics
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    • v.26 no.4
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    • pp.315-353
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    • 2019
  • Orders and types of entire and meromorphic functions have been actively investigated by many authors. In the present paper, we aim at investigating some basic properties in connection with sum and product of relative (p, q)-𝜑 order, relative (p, q)-𝜑 type, and relative (p, q)-𝜑 weak type of meromorphic functions with respect to entire functions where p, q are any two positive integers and 𝜑 : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

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

  • Biswas, Tanmay;Biswas, Chinmay
    • 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.