Uniqueness for Meromorphic Functions Concerning Differential Polynomials

2008 ◽  
Vol 15 (4) ◽  
pp. 731-738
Author(s):  
Chao Meng
Keyword(s):  
Recent Result ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Differential Polynomials ◽  
Weighted Sharing ◽  
Nagoya Math

Abstract Using the notion of weighted sharing of values which was introduced by I. Lahiri [Nagoya Math. J. 161: 193–206, 2001], we deal with the uniqueness problem of meromorphic functions concerning differential polynomials and obtain some theorems which not only improve a recent result of W. L. Xiong, W. C. Lin and S. Mori [Sci. Math. Jpn. 62: 305–315, 2005], but also improve and supplement the result of W. C. Lin and H. X. Yi [Complex Var. Theory Appl. 49: 793–806, 2004].

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.

scholarly journals UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH WEAKLY WEIGHTED SHARING

2013 ◽  
Vol 88 (1) ◽  
pp. 26-43 ◽  
Author(s):  
THAMIR ALZAHARY
Keyword(s):  
Meromorphic Functions ◽  
Differential Polynomials ◽  
Weighted Sharing ◽  
Zeros Of Meromorphic Functions

AbstractIn this paper, we introduce the notion of weakly weighted sharing of zeros of meromorphic functions ignoring multiplicities, which extends the notion of weakly weighted sharing counting multiplicities, and we also introduce the notion of multiplicity. By using these notions, we prove some results on the uniqueness of meromorphic functions concerning differential polynomials sharing nonzero finite values. The results in this paper extend the results of Yang and Hua, Fang, and Dyavanal. In this paper, we correct defective points in the paper of Wu et al. [‘Uniqueness of meromorphic functions sharing one value’, Bull. Aust. Math. Soc. 85(2012), 280–294].

scholarly journals Weighted sharing and uniqueness of memorphic functions with regard to multiplicity

2014 ◽  
Vol 45 (2) ◽  
pp. 165-177
Author(s):  
Pulak Sahoo ◽  
Biswajit Saha
Keyword(s):  
Fixed Point ◽  
Meromorphic Functions ◽  
Differential Polynomials ◽  
Weighted Sharing

In the paper we study the uniqueness problems of meromorphic functions whose certain nonlinear differential polynomials share certain value or fixed point with finite weight and obtain two theorems which improve two recent results due to S.S. Bhoosnurmath and S.R. Kabbur [Tamkang J. Math., 44, 11-22, Spring 2013].

scholarly journals Weighted sharing and uniqueness of meromorphic functions

2014 ◽  
Vol 45 (1) ◽  
pp. 1-12
Author(s):  
Harina P Waghamore ◽  
Tanuja A
Keyword(s):  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Weighted Sharing

In this paper, we study with a weighted sharing method the uniqueness problem of $[f^{n}P(f)]^{(k)}$ and $[g^{n}P(g)]^{(k)}$ sharing one value and obtain some results which extend and improve the results due to Hong-Yan Xu and Ting-Bin Cao.

Uniqueness of Differential Polynomials of Meromorphic Functions Sharing a Small Function Without Counting Multiplicity

2016 ◽  
Vol 57 (1) ◽  
pp. 121-135
Author(s):  
Bui Thi Kieu Oanh ◽  
Ngo Thi Thu Thuy
Keyword(s):  
Nevanlinna Theory ◽  
Complex Analysis ◽  
Meromorphic Functions ◽  
Small Function ◽  
Uniqueness Problem ◽  
Differential Polynomials ◽  
Counting Multiplicity

Abstract The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function without counting multiplicity. The results of this paper are extension of some problems studied by K. Boussaf et. al. in [2] and generalization of some results of S.S. Bhoosnurmath et. al. in [4].

Uniqueness of meromorphic functions sharing a value or small function

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Nguyen Van Thin ◽  
Ha Tran Phuong
Keyword(s):  
Nevanlinna Theory ◽  
Complex Analysis ◽  
Meromorphic Functions ◽  
Small Function ◽  
Uniqueness Problem ◽  
Differential Polynomials ◽  
A Value

AbstractThe paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a value or small function. The results of this paper are generalizations of some problems studied in [BOUSSAF, K.—ESCASSUT, A.—OJEDA, J.:

scholarly journals Non linear differential polynomials sharing fixed points with finite weights

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Abhijit Banerjee ◽  
Pulak Sahoo
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions ◽  
Differential Polynomials ◽  
Weighted Sharing ◽  
Non Linear ◽  
Linear Differential Polynomials ◽  
Linear Differential

AbstractWe employ the notion of weighted sharing to investigate the uniqueness of meromorphic functions when two nonlinear differential polynomials share fixed points. The results of the paper improve and generalize the recent results due to Xu–Lu–Yi [

scholarly journals Certain non-linear differential polynomials sharing a non zero polynomial

2015 ◽  
Vol 7 (1) ◽  
pp. 35-66
Author(s):  
Sujoy Majumder
Keyword(s):  
Meromorphic Functions ◽  
Differential Polynomials ◽  
Weighted Sharing ◽  
Value Sharing ◽  
Non Linear ◽  
Linear Differential Polynomials ◽  
Linear Differential ◽  
Applied Math ◽  
Nonzero Polynomial

Abstract In this paper with the notion of weighted sharing of values we study the uniqueness of nonlinear differential polynomials of meromorphic functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008), 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011), 23-32.].

scholarly journals Differential polynomials of meromorphic functions sharing a set of values

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 457-472
Author(s):  
Pulak Sahoo ◽  
Gurudas Biswas
Keyword(s):  
Computational Analysis ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Differential Polynomials

In this paper, we investigate the uniqueness problem of meromorphic functions when nonlinear differential polynomials generated by them share a set of values with finite weight and obtain some results which generalize the results due to H.Y. Xu [J. Computational Analysis and Applications 16 (2014) 942-954].

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