scholarly journals Generalized Relative Type and Generalized Weak Type of Entire Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Debasmita Dutta
Keyword(s):  
Entire Function ◽  
Weak Type ◽  
Entire Functions ◽  
Relative Growth ◽  
Growth Properties ◽  
Relative Type

We study some relative growth properties of entire functions with respect to another entire function on the basis of generalized relative type and generalized relative weak type.

scholarly journals ON THE MEASUREMENT OF GROWTH PROPERTIES OF ENTIRE AND MEROMORPHIC FUNCTIONS FOCUSING THEIR RELATIVE TYPE AND RELATIVE WEAK TYPE

2017 ◽  
pp. 1011
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas
Keyword(s):  
Meromorphic Functions ◽  
Weak Type ◽  
Entire Functions ◽  
Order Type ◽  
Relative Order ◽  
Relative Growth ◽  
Growth Properties ◽  
Relative Type ◽  
Growth Indicators

The concepts of relative growth indicators such as relative order, relative type, relative weak type, etc. have widely been used to avoid comparing growths of entire and meromorphic functions just with exp functions. Using the notions of several relative growth indicators as mentioned earlier, in this paper we would like to find out the limits in terms of classical growth indicators (i.e. order, type, weak type etc.) in which the relative type, relative weak type, etc. of meromorphic functions with respect to entire functions should lie.

scholarly journals Growth Estimates of Composite Entire Functions in the Light of Slowly Changing Functions Based Relative Order, Relative Type and Relative Weak Type

2015 ◽  
Vol 54 (1) ◽  
pp. 59-74
Author(s):  
S. K. Datta ◽  
T. Biswas ◽  
S. Bhattacharyya
Keyword(s):  
Weak Type ◽  
Entire Functions ◽  
Maximum Modulus ◽  
Relative Order ◽  
Maximum Term ◽  
Growth Properties ◽  
Relative Type

Abstract In the paper we prove some growth properties of maximum term and maximum modulus of composition of entire functions on the basis of relative L*-order, relative L*-type and relative L*-weak type.

scholarly journals On the growth measures of entire and meromorphic functions focusing their generalized relative type and generalized relative weak type

2017 ◽  
Vol 9 (1) ◽  
pp. 53-73
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas
Keyword(s):  
Entire Function ◽  
Meromorphic Functions ◽  
Weak Type ◽  
Relative Order ◽  
Growth Properties ◽  
Relative Type

Abstract In this paper we study some comparative growth properties of composite entire and meromorphic functions on the basis of their generalized relative order, generalized relative type and generalized relative weak type with respect to another entire function.

scholarly journals SUM AND PRODUCT THEOREMS OF RELATIVE TYPE AND RELATIVE WEAK TYPE OF ENTIRE FUNCTIONS

2015 ◽  
Vol 37 (1) ◽  
pp. 65-97 ◽  
Author(s):  
Junesang Choi ◽  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Pulakesh Sen
Keyword(s):  
Weak Type ◽  
Entire Functions ◽  
Relative Type

Relative (p,q)-φ order and relative (p,q)-φ type based on some growth properties of composite p-adic entire functions

2020 ◽  
Vol 29 (1) ◽  
pp. 09-16
Author(s):  
Biswas Tanmay
Keyword(s):  
Weak Type ◽  
Entire Functions ◽  
Closed Field ◽  
Unbounded Function ◽  
Algebraically Closed Field ◽  
Growth Properties ◽  
Positive Integers

Let K be a complete ultrametric algebraically closed field and A (K) be the K-algebra of entire functions 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, relative (p, q)-ϕ type and relative (p, q)-ϕ weak type where p, q are any two positive integers and ϕ (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

scholarly journals Advancement on the study of growth analysis of differential polynomial and differential monomial in the light of slowly increasing functions

2018 ◽  
Vol 10 (1) ◽  
pp. 31-57
Author(s):  
T. Biswas
Keyword(s):  
Growth Analysis ◽  
Meromorphic Functions ◽  
Weak Type ◽  
Differential Polynomial ◽  
Differential Polynomials ◽  
Positive Continuous Function ◽  
Relative Growth ◽  
Growth Properties ◽  
Increasing Functions ◽  
Growth Indicators

Study of the growth analysis of entire or meromorphic functions has generally been done through their Nevanlinna's characteristic function in comparison with those of exponential function. But if one is interested to compare the growth rates of any entire or meromorphic function with respect to another, the concepts of relative growth indicators will come. The field of study in this area may be more significant through the intensive applications of the theories of slowly increasing functions which actually means that $L(ar)\sim L(r)$ as $ r\rightarrow \infty $ for every positive constant $a$, i.e. $\underset{ r\rightarrow \infty }{\lim }\frac{L\left( ar\right) }{L\left( r\right) }=1$, where $L\equiv L\left( r\right) $ is a positive continuous function increasing slowly. Actually in the present paper, we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using the idea of relative $_{p}L^{\ast }$-order, relative $_{p}L^{\ast }$- type, relative $_{p}L^{\ast }$-weak type and differential monomials, differential polynomials generated by one of the factors which extend some earlier results where $_{p}L^{\ast }$ is nothing but a weaker assumption of $L.$

Growth Analysis of Composite Entire Functions of Several Complex Variables Based on Relative Order

2020 ◽  
pp. 151-163
Author(s):  
Balram Prajapati ◽  
Anupama Rastogi
Keyword(s):  
Entire Function ◽  
Lower Order ◽  
Growth Analysis ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Relative Order ◽  
Growth Properties

<p>In this paper we introduce some new results depending on the comparative growth properties of composition of entire function of several complex variables using relative L^*-order, Relative L^*-lower order and L≡L(r_1,r_2,r_3,……..,r_n) is a slowly changing functions. We prove some relation between relative L^*- order and relative L^*- lower order.</p>

On Different Relative Growth Factors of Entire Functions

2020 ◽  
Vol 87 (1-2) ◽  
pp. 37
Author(s):  
Sanjib Kumar Datta ◽  
Banani Dutta ◽  
Nityagopal Biswas
Keyword(s):  
Growth Factors ◽  
Entire Function ◽  
Entire Functions ◽  
Unbounded Function ◽  
Relative Growth

In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.

scholarly journals On Some Growth Properties of Entire Functions Using Their Maximum Moduli Focusingp,qth Relative Order

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Luis Manuel Sanchez Ruiz ◽  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Golok Kumar Mondal
Keyword(s):  
Entire Function ◽  
Growth Rates ◽  
Lower Order ◽  
Entire Functions ◽  
Relative Order ◽  
Growth Properties ◽  
Definition Of ◽  
Positive Integers

We discuss some growth rates of composite entire functions on the basis of the definition of relativep,qth order (relativep,qth lower order) with respect to another entire function which improve some earlier results of Roy (2010) wherepandqare any two positive integers.

Sign in / Sign up

Export Citation Format

Share Document