ERRATUM: ”UNIQUENESS OF MEROMORPHIC FUNCTIONS SHARING TWO FINITE SETS IN C WITH FINITE WEIGHT ”

Abstract

Theorem 1.1. Let S1 = {0, −a
n−1
n
}, S2 = {z : z
n + azn−1 + b = 0} where n(≥ 7)
be an integer and a and b be two nonzero constants such that z
n+azn−1+b = 0 has
no multiple root. If f and g be two non-constant meromorphic functions having no
simple pole such that Ef (S1, 0) = Eg(S1, 0) and Ef (S2, 2) = Eg(S2, 2), then f ≡ g.
Theorem 1.2. Let Si
, i = 1, 2 and f and g be taken as in Theorem 1.1 where
n(≥ 8) is an integer. If Ef (S1, 0) = Eg(S1, 0) and Ef (S2, 1) = Eg(S2, 1), then
f ≡ g.
Next by calculation it can be shown that in Lemma-2.2 we would always have p = 0.
So in Lemma-2.2 we should replace N(r, 0; f |≥ p+1)+N

r, −a
n−1
n
; f |≥ p + 1
by
N(r, 0; f) + N

r, −a
n−1
n
; f

. In that case the statement of the Lemma-2.2. should
be replaced by
Lemma-2.2. Let S1 and S2 be defined as in Theorem 1.1 and F, G be given
by (2.1). If for two non-constant meromorphic functions f and g, Ef (S1, 0) =
Eg(S1, 0), Ef (S2, 0) = Eg(S2, 0), where H 6≡ 0 then
N(r, H) ≤ N(r, 0; f) + N

r, −a
n − 1
n
; f

+ N∗(r, 1; F, G)
+N(r, ∞; f) + N(r, ∞; g) + N0(r, 0; f
0
) + N0(r, 0; g
0
),
where N0(r, 0; f
0
) is the reduced counting function of those zeros of f
0
which are
not the zeros of f

f − a
n−1
n

(F − 1) and N0(r, 0; g
0
) is similarly define

Keywords

• Meromorphic function
• Uniqueness
• Shared Set
• Weighted sharing

References

1. [1] Banerjee, A., Halder, G.: Uniqueness of meromorphic functions sharing two finite sets in $\mathbb{C}$ with finite weight. Konuralp J. Math. 2(2), 42–52 (2014)