Uniqueness of meromorphic functions concerning weakly weighted-sharing

Abstract

In this paper, we introduce the definition of weakly weighted-sharing which is between ''CM'' and ''IM''. Using the notion of weakly weighted-sharing, we study the uniqueness problems on meromorphic function and its kth order derivative f ðkÞ satisfying certain sharing set properties. As consequences, we are able to answer questions posed by Kit-wing Yu, which were also studied by I. Lahiri and A. Sarkar, L. P. Liu and Y. X. Gu. Our results sharpen the above results.

Uniqueness of Meromorphic Functions With Weakly Weighted Sharing

“…Lin and Lin [4] introduced the notion of weakly weighted sharing for CM, as given in the following definition. D 1.1 [4].…”

“…Lin and Lin [4] introduced the notion of weakly weighted sharing for CM, as given in the following definition. D 1.1 [4]. Let k be a positive integer or infinity, and let a be a small function of nonconstant meromorphic functions f and g. We denote by N k) (r, a, f, g) the reduced counting function of those a-points of f , whose multiplicities are equal to the corresponding a-points of g, and both of their multiplicities are less than or equal to k. We say that f and g share (a, k) * CM, if…”

Uniqueness of Meromorphic Functions Sharing a Small Function with Their Differential Polynomials

“…Progress to explore the possible answer of Yu [14] has been remarkable recently, see [1], [9]- [10], [15]- [17]. In 2004, P. Liu and Y. X. Gu [11] provided affirmative answers to the last three questions of Yu [14].…”

“…Obviously if f , g share "(a, k)", then f , g share "(a, p)" for any integer p, 0 ≤ p < k. Also we note that f , g share a "IM" or "CM" if and only if f , g share "(a, 0)" or "(a, ∞)" respectively. With the notion of weakly weighted sharing improving the results of Yu [14] and Liu-Gu [11] Lin and Lin [10] proved the following results.…”

“…In 2006 Lin and Lin [10] introduced the notion of weakly weighted sharing which we shall define next.…”