Meromorphic Functions of Restricted Hyper-Order Sharing One or Two Sets with Its Linear C-Shift Operator

2021 ◽  
Author(s):  
A. Banerjee ◽  
A. Roy
Keyword(s):  
Meromorphic Functions ◽  
Shift Operator ◽  
Hyper Order

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.

On the Distribution of Meromorphic Functions of Positive Hyper-Order

2021 ◽  
Vol 47 (1) ◽  
pp. 243-260
Author(s):  
P. Yang ◽  
S. Wang
Keyword(s):  
Meromorphic Functions ◽  
Hyper Order

Uniqueness and periodicity for meromorphic functions with partial sharing values

2019 ◽  
Vol 69 (1) ◽  
pp. 99-110
Author(s):  
Weichuan Lin ◽  
Shengjiang Chen ◽  
Xiaoman Gao
Keyword(s):  
Uniqueness Theorem ◽  
Meromorphic Functions ◽  
Sharing Values ◽  
Hyper Order

Abstract We prove a periodic theorem of meromorphic functions of hyper-order ρ2(f) < 1. As an application, we obtain the corresponding uniqueness theorem on periodic meromorphic functions. In addition, we show the accuracy of the results by giving some examples.

scholarly journals A note on C. C. Yang's question corresponding to linear shift operator.

2021 ◽  
Vol 13(62) (2) ◽  
pp. 423-432
Author(s):  
Abhijit Banerjee ◽  
Arpita Roy
Keyword(s):  
Meromorphic Functions ◽  
Shift Operator ◽  
Future Research ◽  
Shared Value ◽  
Shift Operators

In this paper, we investigate shared value problems of finite ordered meromorphic functions with the linear shift operators governed by them, which practically provide an answer to Yang’s question. We exhibit a number of examples which will justify some assertions in the paper. Based on some examples relevant with the discussion, we also place a question in the penultimate section for future research.

scholarly journals Entire functions of restricted hyper-order sharing a set of two small functions IM with their linear c-shift operators

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abhijit Banerjee ◽  
Arpita Roy
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shift Operator ◽  
Research Work ◽  
Original Research ◽  
Exponent Of Convergence ◽  
Content Type ◽  
Shift Operators ◽  
Small Functions ◽  
Hyper Order

PurposeThe paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator.Design/methodology/approachStandard methodology for papers in difference and shift operators and value distribution theory have been used.FindingsThe relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers.Originality/valueThis is an original research work.

scholarly journals Uniqueness of meromorphic functions with their reduced linear c-shift operators sharing two or more values or sets

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abhijit Banerjee ◽  
Saikat Bhattacharyya
Keyword(s):  
Complex Plane ◽  
Meromorphic Functions ◽  
Shift Operator ◽  
Future Research ◽  
Weighted Sharing ◽  
Shift Operators ◽  
Extended Complex ◽  
Open Question ◽  
Extended Complex Plane

AbstractIn the paper, we introduce a new notion of reduced linear c-shift operator $L _{c}^{r}\,f$Lcrf, and with the aid of this new operator, we study the uniqueness of meromorphic functions $f(z)$f(z) and $L_{c}^{r}\,f$Lcrf sharing two or more values in the extended complex plane. The results obtained in the paper significantly improve a number of existing results. Further, using the notion of weighted sharing of sets, we deal the same problem. We exhibit a handful number of examples to justify certain statements relevant to the content of the paper. We are also able to determine the form of the function that coincides with its reduced linear c-shift operator. At the end of the paper, we pose an open question for future research.

On Drasin's questions of meromorphic functions of finite hyper-order

2012 ◽  
Vol 42 (11) ◽  
pp. 1095-1114
Author(s):  
HongXun YI ◽  
XiaoMin LI
Keyword(s):  
Meromorphic Functions ◽  
Hyper Order

scholarly journals Existence of Meromorphic Solutions of First-Order Difference Equations

2019 ◽  
Vol 51 (3) ◽  
pp. 465-504
Author(s):  
Risto Korhonen ◽  
Yueyang Zhang
Keyword(s):  
Riccati Equation ◽  
Meromorphic Functions ◽  
Meromorphic Solution ◽  
Elliptic Functions ◽  
Order Difference ◽  
First Order ◽  
Difference Analogue ◽  
Hyper Order ◽  
Natural Difference ◽  
Special Case

AbstractIt is shown that if $$\begin{aligned} f(z+1)^n=R(z,f), \end{aligned}$$f(z+1)n=R(z,f),where R(z, f) is rational in f with meromorphic coefficients and $$\deg _f(R(z,f))=n$$degf(R(z,f))=n, has an admissible meromorphic solution, then either f satisfies a difference linear or Riccati equation with meromorphic coefficients, or the equation above can be transformed into one in a list of ten equations with certain meromorphic or algebroid coefficients. In particular, if $$f(z+1)^n=R(z,f)$$f(z+1)n=R(z,f), where the assumption $$\deg _f(R(z,f))=n$$degf(R(z,f))=n has been discarded, has rational coefficients and a transcendental meromorphic solution f of hyper-order $$<1$$<1, then either f satisfies a difference linear or Riccati equation with rational coefficients, or the equation above can be transformed into one in a list of five equations which consists of four difference Fermat equations and one equation which is a special case of the symmetric QRT map. Solutions to all of these equations are presented in terms of Weierstrass or Jacobi elliptic functions, or in terms of meromorphic functions that are solutions to a difference Riccati equation. This provides a natural difference analogue of Steinmetz’ generalization of Malmquist’s theorem.

scholarly journals A Picard type theorem concerning meromorphic functions of\\ hyper-order

2016 ◽  
Vol 47 (3) ◽  
pp. 357-370 ◽  
Author(s):  
PANG XueCheng ◽  
YANG Pai ◽  
NIU PeiYan
Keyword(s):  
Meromorphic Functions ◽  
Type Theorem ◽  
Hyper Order ◽  
Picard Type Theorem
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