scholarly journals Unique Range Set for Meromorphic Functions with Deficient Values

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Abhijit Banerjee ◽  
Sujoy Majumder
Keyword(s):  
Meromorphic Functions ◽  
Weighted Sharing ◽  
Unique Range Set

We employ the idea of weighted sharing of sets to find a unique range set for meromorphic functions with deficient values. Our result improves, generalises, and extends the result of Lahiri. Examples are exhibited that a condition in one of our results is the best possible one.

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 The Unique Range Set of Meromorphic Functions in an Angular Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hong-Yan Xu ◽  
Zu-Xing Xuan ◽  
Hua Wang
Keyword(s):  
Meromorphic Functions ◽  
Angular Domain ◽  
Shared Set ◽  
Unique Range Set

By using Tsuji's characteristic, we investigate uniqueness of meromorphic functions in an angular domain dealing with the shared set, which is different from the set of the paper (Lin et al., 2006) and obtain a series of results about the unique range set of meromorphic functions in angular domain.

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

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.

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