# zbMATH — the first resource for mathematics

Meromorphic functions sharing fixed points and poles with finite weights. (English) Zbl 1295.30074
Summary: With the aid of the weighted sharing method we study problems of meromorphic functions that share fixed points (or a nonzero finite value) and poles with finite weights. The results of the paper improve some recent results due to Y.-H. Cao and X.-B. Zhang [J. Inequal. Appl. 2012, Article ID 100, 10 p. (2012; Zbl 1291.30193)].

##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text:
##### References:
 [1] T. C. Alzahary, H. X. Yi, Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl., 49 (2004), 1063-1078. · Zbl 1067.30055 [2] A. Banerjee, Uniqueness of meromorphic functions sharing two sets with finite weight, Port. Math. (N.S.) 65 (2008), 81-93. · Zbl 1146.30014 [3] W. Bergweiler, A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoame., 11 (1995), 355-373. · Zbl 0830.30016 [4] Y. H. Cao, X. B. Zhang, Uniqueness of meromorphic functions sharing two values, J. Inequal. Appl., 2012:100. · Zbl 1291.30193 [5] H. H. Chen, M. L. Fang, The value distribution of fnf1, Sci. China Math., 38 (1995), 789-798. · Zbl 0839.30026 [6] M. L. Fang, A note on a problem of Hayman, Analysis (Munich), 20 (2000), 45-49. · Zbl 0948.30030 [7] M. L. Fan, H. L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl., 268 (2002), 426-439. · Zbl 1030.30028 [8] W. K. Hayman, Meromorphic functions, The Clarendon Press, Oxford (1964). · Zbl 0115.06203 [9] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-206. · Zbl 0981.30023 [10] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241-253. · Zbl 1025.30027 [11] P. Sahoo, Meromorphic functions that share fixed points with finite weights, Bull. Math. Anal. Appl., 2 (2010), 106-118. · Zbl 1312.30049 [12] J. F. Xu, Z. L. Zhang, Some inequalities of differential polynomials, Math. Inequal. Appl., 12 (2009), 99-113. · Zbl 1169.30314 [13] C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107-112. · Zbl 0217.38402 [14] C. C. Yang, X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406. · Zbl 0890.30019 [15] L. Yang, Value distribution theory, Springer- Verlag, Berlin, 1993. · Zbl 0790.30018 [16] H. X. Yi, C. C. Yang, Uniqueness theory of meromorphic functions, Science Press, Beijing, 1995. [17] L. Zalcman, On some problems of Hayman, Preprint (Bar-Ilan University), 1995. [18] J. L. Zhang, L. Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8 (2007), Art. 18. · Zbl 1136.30009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.