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

Authors : Abhijit Banerjee, Goutam Haldar

Pages : 168-171

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Publication Date : 2017-10-15

Article Type : Research

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