Mathematica Bohemica, Vol. 143, No. 3, pp. 277-289, 2018
A note on some results of Li and Li
Sujoy Majumder, Somnath Saha
Received December 18, 2016. First published October 19, 2017.
Abstract: The purpose of the paper is to study the uniqueness problems of linear differential polynomials of entire functions sharing a small function and obtain some results which improve and generalize the related results due to J. T. Li and P. Li (2015). Basically we pay our attention to the condition $\lambda(f)\not=1$ in Theorems 1.3, 1.4 from J. T. Li and P. Li (2015). Some examples have been exhibited to show that conditions used in the paper are sharp.
Keywords: entire function; linear differential polynomial; uniqueness
References: [1] A. Banerjee: Meromorphic functions sharing one value. Int. J. Math. Math. Sci. 22 (2005), 3587-3598. DOI 10.1155/IJMMS.2005.3587 | MR 2205158 | Zbl 1093.30024 [2] W. K. Hayman: Meromorphic Functions. Oxford Mathematical Monographs. Clarendon Press, Oxford (1964). MR 0164038 | Zbl 0115.06203 [3] H. Herold: Differentialgleichungen im Komplexen. Studia Mathematica. Skript 2. Vandenhoeck & Ruprecht, Göttingen (1975). MR 0470293 | Zbl 03505407 [4] X. H. Hua: A unicity theorem for entire functions. Bull. Lond. Math. Soc. 22 (1990), 457-462. DOI 10.1112/blms/22.5.457 | MR 1082015 | Zbl 0714.30030 [5] I. Lahiri: Uniqueness of meromorphic functions as governed by their differential polynomials. Yokohama Math. J. 44 (1997), 147-156. MR 1453358 | Zbl 0884.30023 [6] I. Lahiri: Weighted value sharing and uniqueness of meromorphic functions. Complex Variables, Theory Appl. 46 (2001), 241-253. DOI 10.1080/17476930108815411 | MR 1869738 | Zbl 1025.30027 [7] I. Laine: Nevanlinna Theory and Complex Differential Equations. De Gruyter Studies in Mathematics 15. Walter de Gruyter, Berlin (1993). MR 1207139 | Zbl 0784.30002 [8] J.-T. Li, P. Li: Uniqueness of entire functions concerning differential polynomials. Commun. Korean Math. Soc. 30 (2015), 93-101. DOI 10.4134/CKMS.2015.30.2.093 | MR 3346483 | Zbl 1320.30059 [9] E. Mues, M. Reinders: On a question of C. C. Yang. Complex Variables, Theory Appl. 34 (1997), 171-179. DOI 10.1080/17476939708815045 | MR 1473597 | Zbl 0948.30036 [10] K. Shibazaki: Unicity theorems for entire functions of finite order. Mem. Natl. Def. Acad. 21 (1981), 67-71. Zbl 0507.30022 [11] C. C. Yang: On two entire functions which together with their first derivatives have the same zeros. J. Math. Anal. Appl. 56 (1976), 1-6. DOI 10.1016/0022-247X(76)90002-0 | MR 0419761 | Zbl 0338.30018 [12] C. C. Yang, H. X. Yi: On the unicity theorem for meromorphic functions with deficient values. Acta Math. Sin. 37 (1994), 62-72. (In Chinese.) MR 1272506 | Zbl 0804.30026 [13] C. C. Yang, H. X. Yi: Uniqueness Theory of Meromorphic Functions. Mathematics and Its Applications 557. Kluwer Academic Publishers, Dordrecht (2003). MR 2105668 | Zbl 1070.30011 [14] H. X. Yi: A question of C. C. Yang on the uniqueness of entire functions. Kodai Math. J. 13 (1990), 39-46. DOI 10.2996/kmj/1138039158 | MR 1047593 | Zbl 0707.30022 [15] H. X. Yi: Uniqueness of meromorphic functions and a question of C. C. Yang. Complex Variables, Theory Appl. 14 (1990), 169-176. DOI 10.1080/17476939008814415 | MR 1048716 | Zbl 0701.30025 [16] H. X. Yi: Meromorphic functions that share one or two values. Complex Variables, Theory Appl. 28 (1995), 1-11. DOI 10.1080/17476939508814833 | MR 1700258 | Zbl 0841.30027 [17] J.-L. Zhang, L.-Z. Yang: Some results related to a conjecture of R. Brück. JIPAM J. Inequal. Pure Appl. Math. 8 (2007), Article No. 18, 11 pages. MR 2295712 | Zbl 1136.30009
Affiliations: Sujoy Majumder, Department of Mathematics, Raiganj University, Raiganj, West Bengal-733134, India, e-mail: sujoy.katwa@gmail.com, sm05math@gmail.com; Somnath Saha, Mehendipara Jr. High School, Hili Balurghat Hwy, Arazi Huzuri Kasba, P.O.-Daulatpur, West Bengal-733125, India, e-mail: somnathsaha.87@gmail.com
