Weighted sharing and uniqueness of meromorphic functions

Waghamore, Harina P.; Tanuja, A.

doi:10.5556/j.tkjm.45.2014.938

Cited by 1 publication

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“…Lemma 2.9. [9] Let f and g be two non-constant meromorphic functions and let n(≥ 1),k(≥ 1), and m(≥ 1) be integers. Then F G = 1, where F , G are as define above.…”

Section: Lemmasmentioning

confidence: 99%

On Uniqueness of L-Sharing of Differential Polynomials of Meromorphic Functions

Mandal¹,

Shaw²

2020

Adv. Math., Sci. J.

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In this paper, we shall study the uniqueness problems of differential polynomials of meromorphic functions sharing 1 value. Here we prove two uniqueness theorems which extend and improve recent results of H.P. Waghamore and N.H. Sannappala [10]. 1 corresponding author 2010 Mathematics Subject Classification. 30D35. 119 120 N. MANDAL AND A. SHAWm ≤ l and l + 1 times if m > l. If E l (a, f ) = E l (a, g), then we say that f and g share the value a with weight l. We also use the notation N (r, a; f |p) to denote the counting function of f − a where m fold zeros is counted m times if m ≤ p and p times if m > p , where p is an integer. Definition 1.1. [4] Let f is a nonconstant meromorphic function and a ∈ C ∪ {∞}, the counting function of a-points of f with multiplicities at least p(∈ Z + ) is denoted by N (r, a; f |≥ p) and N (r, a; f |≥ p) is the corresponding reduced counting function. Similarly we can define N (r, a; f |≤ p) and N (r, a; f |≤ p). Definition 1.2. [4] The counting function of a-points of f , where an a-point of multiplicities m is counted m times if m ≤ p and p times if m > p is denoted by N p (r, a; f ), where p ∈ Z + ∪ {∞}. Then we can write:

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“…Lemma 2.9. [9] Let f and g be two non-constant meromorphic functions and let n(≥ 1),k(≥ 1), and m(≥ 1) be integers. Then F G = 1, where F , G are as define above.…”

Section: Lemmasmentioning

confidence: 99%