scholarly journals Results on weighted sharing of values for meromorphic functions

2007 ◽  
Vol 92 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Xiao-Min Li ◽  
Hong-Xun Yi
Keyword(s):  
Meromorphic Functions ◽  
Weighted Sharing

Uniqueness of meromorphic functions sharing two sets with finite weight ii

2010 ◽  
Vol 41 (4) ◽  
pp. 379-392
Author(s):  
Abhijit Banerjee
Keyword(s):  
Present Author ◽  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Weighted Sharing

With the help of the notion of weighted sharing of sets we deal with the well known question of Gross and prove some uniqueness theorems on meromorphic functions sharing two sets. Our results will improve and supplement some recent results of the present author.

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.

scholarly journals LINEAR DIFFERENTIAL POLYNOMIALS WEIGHTED-SHARING A SET OF ROOTS OF UNITY

2021 ◽  
pp. 333
Author(s):  
Dilip Chandra Pramanik ◽  
Jayanta Roy
Keyword(s):  
Meromorphic Functions ◽  
Roots Of Unity ◽  
Differential Polynomials ◽  
Weighted Sharing ◽  
Linear Differential Polynomials ◽  
Linear Differential

In this paper, we study the uniqueness of linear diFFerential polynomials of meromorphic functions when they share a set of roots of unity. Our results shall generalize recent results.

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