The uniqueness problem for meromorphic functions in the unit disc sharing values and a set in an angular domain

“…Let z 0 be a zero of f with multiplicity p 0 . Then from (17), we see that z 0 is a pole of (say with multiplicity q 0 ). Thus, we have np 0 + p 0 − 1 = nq 0 + 3q 0 + q 0 + 1, i.e., 3q 0 + 2 = (n + 1)(p 0 − q 0 ) ≥ n + 1, i.e., q 0 ≥ n−1 3 .…”

Section: Lemmasmentioning

confidence: 98%

“…Many research works on differential polynomials of meromorphic functions sharing certain value have been done by many mathematicians worldwide (see [1], [3], [10], [12], [14], [15], [16], [17], [19], [20]). Recently, there have been an increasing interest in studying differential polynomials of meromorphic functions sharing a set of values.…”

mentioning

confidence: 99%

Differential polynomials of meromorphic functions sharing a set of values

Sahoo

Biswas²

2018

Filomat

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In this paper, we investigate the uniqueness problem of meromorphic functions when nonlinear differential polynomials generated by them share a set of values with finite weight and obtain some results which generalize the results due to H.Y. Xu [ J. Computational Analysis and Applications 16 (2014) 942-954]. 1. Introduction, Definitionnitions and Results In this paper, by meromorphic function we shall always mean meromorphic function in the complex plane. We shall use the standard notations of the Nevanlinna's theory of meromorphic functions as explained in [4], [5] and [21]. For a nonconstant meromorphic function f , we denote by T(r, f) the Nevanlinna Characteristic function of f and by S(r, f) any quantity satisfying S(r, f) = o{T(r, f)} for all r outside a possible exceptional set of finite logarithmic measure. For a ∈ C ∪ {∞} and S ⊂ C ∪ {∞}, we define E(S, f) = a∈S {z : f (z) − a = 0, counting multiplicity}, E(S, f) = a∈S {z : f (z) − a = 0, ignoring multiplicity}. Let f and be two nonconstant meromorphic functions. If E(S, f) = E(S,), we say that f and share the set S CM and if E(S, f) = E(S,), we say that f and share the set S IM. Especially if S = {a}, we say that f and share the value a CM when E(S, f) = E(S,) and a IM when E(S, f) = E(S,). Let k be a positive integer or infinity. For a ∈ C ∪ {∞}, we denote by E k) (a, f) the set of all a-points of f whose multiplicities are not greater than k. Also by E k) (a, f), we denote the set of all distinct a-points of f whose multiplicities are not greater than k. If E ∞) (a, f) = E ∞) (a,), we say that f and share the value a CM and if E ∞) (a, f) = E ∞) (a,), we say that f and share the value a IM. For a ∈ C ∪ {∞} and S ⊂ C ∪ {∞}, we define E k) (S, f) = a∈S E k) (a, f) and E k) (S, f) = a∈S E k) (a, f).

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The uniqueness problem for meromorphic functions in the unit disc sharing values and a set in an angular domain

Cited by 4 publications

References 14 publications

Unicity Theorem for Higher Order Derivatives of Meromorphic Functions on Annuli Dilip Chandra Pramanik and Jayanta Roy

Unicity Theorem for Higher Order Derivatives of Meromorphic Functions on Annuli Dilip Chandra Pramanik and Jayanta Roy

Nevanlinna’s Five Values Theorem on Annuli

Differential polynomials of meromorphic functions sharing a set of values

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