A uniqueness result related to certain non-linear differential polynomials sharing the same 1-points

Abstract

ABSTRACT. The purpose of the paper is to study the uniqueness of meromorphic function when certain non-linear differential polynomials share the same 1-points. As a consequence of the main result we improve and supplement the following recent result: [LAHIRI, I.-PAL, R.: Nonlinear differential polynomials sharing 1

Uniqueness of meromorphic functions concerning differential polynomials share one value

“…In 2008, Banerjee [6] proved the following theorem. Theorem D. Let f and g be two transcendental meromorphic functions, and let n, k be two positive integers with n ≥ 9k + 14.…”

Nonlinear differential polynomials sharing a non-zero polynomial with finite weight

“…DOI: 10.21136/MB.2016. 2 satisfying S(r) = O(T (r)) as r → ∞, outside a possible exceptional set of finite linear measure.…”

Non-linear differential polynomials sharing small function with finite weight

“…Theorem G. [5] Let f and g be two transcendental meromorphic functions, whose zeros and poles are of multiplicities at least s, where s is a positive integer. Let ( f n ) (k) and (g n ) (k) The possibility [ f n (a 1 f 2 + a 2 f + a 3 )] (k) [g n (a 1 g 2 + a 2 g + a 3 )] (k) ≡ b 2 does not occur for k = 1. Now from the above discussion the following questions are inevitable.…”