scholarly journals Effect of generalized relative order on the growth of composite entire functions

2015 ◽  
Vol 64 (1) ◽  
pp. 39-59
Author(s):  
KUMAR DATTA ◽  
Sanjib Sanjib ◽  
Tanmay Tanmay ◽  
Chinmay Chinmay
Keyword(s):  
Entire Functions ◽  
Relative Order

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 A Note on Relative $(p,q)$ th Proximate Order of Entire Functions

2016 ◽  
Vol 8 (5) ◽  
pp. 1
Author(s):  
Luis Manuel Sanchez Ruiz ◽  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Chinmay Ghosh
Keyword(s):  
Entire Function ◽  
Physical State ◽  
Entire Functions ◽  
Relative Order ◽  
Proximate Order ◽  
Positive Integers

Relative order of functions measures specifically how different in growth two given functions are which helps to settle the exact physical state of a system. In this paper for any two positive integers $p$ and $q,$ we introduce the notion of relative $(p,q)$ th proximate order of an entire function with respect to another entire function and prove its existence.

scholarly journals Growth Rates of Meromorphic Functions Focusing Relative Order

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Sarmila Bhattacharyya
Keyword(s):  
Growth Rates ◽  
Meromorphic Functions ◽  
Entire Functions ◽  
Relative Order ◽  
Made In

A detailed study concerning some growth rates of composite entire and meromorphic functions on the basis of their relative orders (relative lower orders) with respect to entire functions has been made in this paper.

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 basic properties of generalized relative order of entire functions

2017 ◽  
Vol 2 (5) ◽  
pp. 242-251
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Jinarul Haque Shaikh
Keyword(s):  
Entire Functions ◽  
Relative Order ◽  
Basic Properties
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