scholarly journals An entire function sharing fixed points with its linear differential polynomial

2018 ◽  
Vol 22 (1) ◽  
pp. 125-136
Author(s):  
Imrul Kaish ◽  
Indrajit Lahiri
Keyword(s):  
Entire Function ◽  
Fixed Points ◽  
Entire Functions ◽  
Differential Polynomial ◽  
Differential Polynomials ◽  
Linear Polynomial ◽  
Linear Differential Polynomial ◽  
Linear Differential Polynomials ◽  
Linear Differential ◽  
Function Sharing

We study the uniqueness of entire functions, when they share a linear polynomial, in particular, fixed points, with their linear differential polynomials.

AN ENTIRE FUNCTION SHARING TWO VALUES WITH ITS LINEAR DIFFERENTIAL POLYNOMIAL

2017 ◽  
Vol 97 (2) ◽  
pp. 265-273
Author(s):  
INDRAJIT LAHIRI
Keyword(s):  
Entire Function ◽  
Differential Polynomial ◽  
Value Sharing ◽  
Linear Differential Polynomial ◽  
Linear Differential ◽  
Function Sharing

We consider the uniqueness of an entire function and a linear differential polynomial generated by it. One of our results improves a result of Li and Yang [‘Value sharing of an entire function and its derivatives’, J. Math. Soc. Japan51(4) (1999), 781–799].

Entire functions sharing a linear polynomial with linear differential polynomials

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6461-6471
Author(s):  
Goutam Ghosh
Keyword(s):  
Present Author ◽  
Entire Functions ◽  
Differential Polynomials ◽  
Linear Polynomial ◽  
Linear Differential Polynomials ◽  
Kodai Math ◽  
Linear Differential

In the paper we study the uniqueness of entire functions sharing a linear polynomial with linear differential polynomials generated by them. The results of the paper improves the corresponding results of P. Li (Kodai Math J. 22: 446-457, 1999), Lahiri-Present author(G. K. Ghosh) (Analysis (Munich)31: 331-340,2011) and Lahiri-Mukherjee(Bull. Aust. Math. Soc. 85: 295-306, 2012).

A Non-zero Value Shared by an Entire Function and its Linear Differential Polynomials

2013 ◽  
Vol 56 (4) ◽  
pp. 769-784
Author(s):  
Indrajit Lahiri ◽  
Imrul Kaish
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Differential Polynomials ◽  
Linear Differential Polynomials ◽  
Linear Differential

Abstract.In this paper we study uniqueness of entire functions sharing a non-zero finite value with linear differential polynomials and address a result of W.Wang and P. Li.

scholarly journals On entire solutions of a certain type of nonlinear differential equation

2001 ◽  
Vol 64 (3) ◽  
pp. 377-380 ◽  
Author(s):  
Chung-Chun Yang
Keyword(s):  
Differential Equation ◽  
Entire Function ◽  
Finite Order ◽  
Nonlinear Differential Equation ◽  
Entire Solution ◽  
Differential Polynomial ◽  
Entire Solutions ◽  
Value Distribution Theory ◽  
Linear Differential Polynomial ◽  
Linear Differential

In this note, we shall study, via Nevanlinna's value distribution theory, the uniqueness of transcendental entire solutions of the following type of nonlinear differential equation: (*) L (f (z)) – p (z) fn(z) = h (z), where L (f) denotes a linear differential polynomial in f with polynomials as its co-efficients, p (z) a polynomial (≢ 0), h an entire function, and n an integer ≥ 3. We show that if the equation (*) has a finite order transcendental entire solution, then it must be unique, unless L (f) ≡ 0.

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