"Some comparative growth properties of meromorphic function in the light of generalized relative order (α,β)"

2021 ◽  
Vol 30 (2) ◽  
pp. 149-156
Author(s):  
TANMAY BISWAS ◽  
◽  
CHINMAY BISWAS ◽  
Keyword(s):  
Meromorphic Function ◽  
Relative Order ◽  
Growth Properties

scholarly journals On the(p,q)th Relative Order Oriented Growth Properties of Entire Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Luis Manuel Sánchez Ruiz ◽  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Golok Kumar Mondal
Keyword(s):  
Quantitative Assessment ◽  
Entire Functions ◽  
Relative Order ◽  
Order Of Growth ◽  
Alternative Definition ◽  
Oriented Growth ◽  
Growth Properties ◽  
Self Similar ◽  
Definition Of ◽  
Positive Integers

The relative order of growth gives a quantitative assessment of how different functions scale each other and to what extent they are self-similar in growth. In this paper for any two positive integerspandq, we wish to introduce an alternative definition of relative(p,q)th order which improves the earlier definition of relative(p,q)th order as introduced by Lahiri and Banerjee (2005). Also in this paper we discuss some growth rates of entire functions on the basis of the improved definition of relative(p,q)th order with respect to another entire function and extend some earlier concepts as given by Lahiri and Banerjee (2005), providing some examples of entire functions whose growth rate can accordingly be studied.

Some growth properties of composite p-adic entire functions on the basis of their relative order and relative lower order

2019 ◽  
Vol 12 (03) ◽  
pp. 1950044
Author(s):  
Tanmay Biswas
Keyword(s):  
Growth Rates ◽  
Lower Order ◽  
Entire Functions ◽  
Closed Field ◽  
Relative Order ◽  
Algebraically Closed Field ◽  
Growth Properties

Let [Formula: see text] be a complete ultrametric algebraically closed field and [Formula: see text] be the [Formula: see text]-algebra of entire functions on [Formula: see text]. For [Formula: see text], [Formula: see text], we wish to introduce the notions of relative order and relative lower order of [Formula: see text] with respect to [Formula: see text]. Hence, after proving some basic results, in this paper, we estimate some growth rates of composite p-adic entire functions on the basis of their relative orders and relative lower orders.

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 Comparative growth analysis of Wronskians in the light of their relative orders

2015 ◽  
Vol 14 (1) ◽  
pp. 135-148
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Ahsanul Hoque
Keyword(s):  
Lower Order ◽  
Growth Analysis ◽  
Meromorphic Functions ◽  
Relative Order ◽  
Growth Properties

Abstract In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.

scholarly journals Derivation of Some Results on the Generalized Relative Orders of Meromorphic Functions

2017 ◽  
Vol 55 (1) ◽  
pp. 51-61
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Lower Order ◽  
Meromorphic Functions ◽  
Relative Order

Abstract In this paper we intend to find out relative order (relative lower order) of a meromorphic function f with respect to another entire function g when generalized relative order (generalized relative lower order) of f and generalized relative order (generalized relative lower order) of g with respect to another entire function h are given.

scholarly journals Some growth properties of wronskians using their relative order

2013 ◽  
pp. 91-99
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Sultan Ali
Keyword(s):  
Relative Order ◽  
Growth Properties

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>

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 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.

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