scholarly journals On some sufficient conditions for periodicity of meromorphic function under new shared sets

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6055-6072
Author(s):  
Abhijit Banerjee ◽  
Molla Ahamed
Keyword(s):  
Meromorphic Function ◽  
Shift Operator ◽  
Sufficient Conditions ◽  
Shared Sets ◽  
Set Sharing

This paper deals with the two set sharing problem related to the uniqueness of a function and its shift operator. With the help of two new range sets we shall significantly improve a number of results in the literature. At the last section we shall exhibit certain examples to show that some conditions used in our results are the best possible.

Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets

2019 ◽  
Vol 69 (3) ◽  
pp. 557-572
Author(s):  
Abhijit Banerjee ◽  
Molla Basir Ahamed
Keyword(s):  
Meromorphic Function ◽  
Shift Operator ◽  
Uniqueness Problem ◽  
Shared Set ◽  
Shared Sets

Abstract Taking two and three shared set problems into background, the uniqueness problem of a meromorphic function together with its shift operator have been studied. Our results will improve a number of recent results in the literature. Some examples have been provided in the last section to show that certain conditions used in the paper, is the best possible.

scholarly journals A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value

2021 ◽  
Vol 55 (1) ◽  
pp. 57-63
Author(s):  
A. Banerjee ◽  
A. Roy
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Shift Operator ◽  
Small Function ◽  
A Value ◽  
Hyper Order

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing a small function together with a value which improve and complement some earlier results. In particular, more or less we have improved and extended two results of Qi-Yang [Meromorphic functions that share values with their shifts or their $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling the superfluous conclusions in them.

scholarly journals On the Uniqueness of Power of a Meromorphic Function Sharing a set with its k-Th Derivative

2018 ◽  
Vol 85 (1-2) ◽  
pp. 1
Author(s):  
Abhijit Banerjee ◽  
Bikash Chakraborty
Keyword(s):  
Meromorphic Function ◽  
Small Functions ◽  
Set Sharing ◽  
Function Sharing

<p>In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more general settings namely set sharing.</p>

ZEROS OF ULTRAMETRIC MEROMORPHIC FUNCTIONS f′ fn(f − a)k − α

2008 ◽  
Vol 01 (03) ◽  
pp. 415-429 ◽  
Author(s):  
Jacqueline Ojeda
Keyword(s):  
Meromorphic Function ◽  
Characteristic Zero ◽  
Meromorphic Functions ◽  
Sufficient Conditions ◽  
Small Function ◽  
Closed Field ◽  
Open Disk ◽  
Algebraically Closed Field ◽  
Absolute Value ◽  
Special Value

Let 𝕂 be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. Similarly to the Hayman problem, here we study meromorphic functions in 𝕂 or in an open disk that are of the form f′ fn(f − a)k − α with α a small function, in order to find sufficient conditions on n, k assuring that they have infinitely many zeros. We first define and characterize a special value for a meromorphic function and check that, if it exists, it is unique. So, such values generalize Picard exceptional values.

scholarly journals On Newp-Valent Meromorphic Function Involving Certain Differential and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Aabed Mohammed ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Meromorphic Function ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Integral Operators

We define new subclasses of meromorphicp-valent functions by using certain differential operator. Combining the differential operator and certain integral operator, we introduce a generalp-valent meromorphic function. Then we prove the sufficient conditions for the function in order to be in the new subclasses.

A note on roots of Markov shifts

1976 ◽  
Vol 13 (03) ◽  
pp. 591-596
Author(s):  
S. M. Rudolfer
Keyword(s):  
Markov Chain ◽  
Shift Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Markov Chain ◽  
Markov Shifts ◽  
Necessary And Sufficient

Let Tv be the two-sided shift operator associated with a finite Markov chain of period v; Using results of Krengel and Michel and Adler, Shields and Smorodinsky, necessary and sufficient conditions for the existence of an rth root of Tv are obtained. In particular, if the Markov chain is irreducible, then Tv has an rth root when and only when (r, v) = 1.

A note on roots of Markov shifts

1976 ◽  
Vol 13 (3) ◽  
pp. 591-596
Author(s):  
S. M. Rudolfer
Keyword(s):  
Markov Chain ◽  
Shift Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Markov Chain ◽  
Markov Shifts ◽  
Necessary And Sufficient

Let Tv be the two-sided shift operator associated with a finite Markov chain of period v; Using results of Krengel and Michel and Adler, Shields and Smorodinsky, necessary and sufficient conditions for the existence of an rth root of Tv are obtained. In particular, if the Markov chain is irreducible, then Tv has an rth root when and only when (r, v) = 1.

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