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

Authors : Abhijit BANERJEE, Goutam HALDAR

Pages : 168-171

View : 13 | Download : 8

Publication Date : 2017-10-15

Article Type : Research Paper

Abstract :Theorem 1.1. Let S1 = {0, −a n−1 n }, S2 = {z : z n + azn−1 + b = 0} where ninsert ignore into journalissuearticles values(≥ 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 insert ignore into journalissuearticles values(S1, 0); = Eginsert ignore into journalissuearticles values(S1, 0); and Ef insert ignore into journalissuearticles values(S2, 2); = Eginsert ignore into journalissuearticles values(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 ninsert ignore into journalissuearticles values(≥ 8); is an integer. If Ef insert ignore into journalissuearticles values(S1, 0); = Eginsert ignore into journalissuearticles values(S1, 0); and Ef insert ignore into journalissuearticles values(S2, 1); = Eginsert ignore into journalissuearticles values(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 Ninsert ignore into journalissuearticles values(r, 0; f |≥ p+1);+N r, −a n−1 n ; f |≥ p + 1 by Ninsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(2.1);. If for two non-constant meromorphic functions f and g, Ef insert ignore into journalissuearticles values(S1, 0); = Eginsert ignore into journalissuearticles values(S1, 0);, Ef insert ignore into journalissuearticles values(S2, 0); = Eginsert ignore into journalissuearticles values(S2, 0);, where H 6≡ 0 then Ninsert ignore into journalissuearticles values(r, H); ≤ Ninsert ignore into journalissuearticles values(r, 0; f); + N r, −a n − 1 n ; f + N∗insert ignore into journalissuearticles values(r, 1; F, G); +Ninsert ignore into journalissuearticles values(r, ∞; f); + Ninsert ignore into journalissuearticles values(r, ∞; g); + N0insert ignore into journalissuearticles values(r, 0; f 0 ); + N0insert ignore into journalissuearticles values(r, 0; g 0 );, where N0insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(F − 1); and N0insert ignore into journalissuearticles values(r, 0; g 0 ); is similarly define
Keywords : Meromorphic function, Uniqueness, Shared Set, Weighted sharing