UNIQUENESS OF P(f) AND [P(f)](k) CONCERNING WEAKLY WEIGHTED SHARING
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In this paper, with the help of the idea of weakly weighted sharing introduced by Lin and Lin [Kodai Math. J. 29(2006), 269-280], we study the uniqueness of polynomial expression P(f) and its derivatives [P(f)](k) of meromorphic functions f sharing a small function. The main results in the paper significantly improved the result of Liu and Gu [Kodai Math. J. 27(3)(2004), 272-279]. This research work finds certain condition under which the polynomial P(f) is reduced to a non-zero monomial and consequently, the class of the function f is characterized. Examples have been exhibited to show that some conditions in the main results simply can not be removed and also some inequalities are sharp.
Abstract
In this paper, with the help of the idea of weakly weighted sharing introduced by Lin and Lin [Kodai Math. J. 29(2006), 269-280], we study the uniqueness of polynomial expression P(f) and its derivatives [P(f)](k) of meromorphic functions f sharing a small function. The main results in the paper significantly improved the result of Liu and Gu [Kodai Math. J. 27(3)(2004), 272-279]. This research work finds certain condition under which the polynomial P(f) is reduced to a non-zero monomial and consequently, the class of the function f is characterized. Examples have been exhibited to show that some conditions in the main results simply can not be removed and also some inequalities are sharp.
참고문헌 (23)
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