Further investigations on a question of Zhang and Lü

Abstract

Abstract. In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

Uniqueness of a Polynomial and a Differential Monomial Sharing a Small Function

“…In [1, Example 1.13], Banerjee-Chakraborty ( [1]) have shown that f n can't be replaced by an arbitrary polynomial P [f ] = a 0 f n + a 1 f n−1 + . .…”

“…Observing Example 1.13 in [1] we note that f (z) = e z , P (f ) = f 2 + 2f and M [f ] = f (3) . So P + 1 = (M + 1) 2 .…”

“…. On the basis of this observation in ( [1]) following question was asked in [1] Question 1.2. Is it possible to replace f n by arbitrary polynomial P [f ] = a 0 f n + a 1 f n−1 + .…”

Uniqueness of power of ameromorphic functionwith its differential polynomial

“…In recent years, many results have been published concerning the above conjecture, (see, [2,3,4,5,6,8,10,11,16,17,18]). Next we recall the following definitions: (i) N (r, a; f |≥ p) (resp.…”

Some uniqueness results related to the Brück conjecture

“…[3] If F and G share(1, l), then N L (r, 1; F ) ≤ 1 (r, ∞; F ) + 1 (r, 0; F ) + S(r, F ) when l ≥ 1, and N L (r, 1; F ) ≤ N (r, ∞; F ) + N (r, 0; F ) + S(r, F ) when l = 0.Lemma 2.12 [3]. Let F and G share (1, l) and H ≡ 0.…”