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Some uniqueness results related to the Brück conjecture

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Abstract Let f be a non-constant meromorphic function and let a = a ⁢ ( z ) {a=a(z)} ( ≢ 0 , ∞ {\not\equiv 0,\infty} ) be a small function… Click to show full abstract

Abstract Let f be a non-constant meromorphic function and let a = a ⁢ ( z ) {a=a(z)} ( ≢ 0 , ∞ {\not\equiv 0,\infty} ) be a small function of f. Under certain essential conditions, we obtained a conclusion similar to the Brück Conjecture, when f and its differential polynomial P ⁢ [ f ] {P[f]} shares a with weight l ( ≥ 0 {\geq 0} ). Our result improves and generalizes a recent result of Li, Yang and Liu [N. Li, L. Yang and K. Liu, A further result related to a conjecture of R. Brück, Kyungpook Math. J. 56 2016, 2, 451–464].

Keywords: conjecture; related conjecture; result; results related; uniqueness results

Journal Title: Analysis
Year Published: 2018

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