Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
angular domain; meromorphic function; unique range set
angular domain; meromorphic function; unique range set
Summary:
We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.
References:
[1] Banerjee, A., Bhattacharjee, P.: Uniqueness and set sharing of derivatives of meromorphic functions. Math. Slovaca 61 (2011), 197-214. DOI 10.2478/s12175-011-0005-6 | MR 2786694 | Zbl 1265.30141
[2] Banerjee, A., Lahiri, I.: A uniqueness polynomial generating a unique range set and vice versa. Comput. Methods Funct. Theory 12 (2012), 527-539. DOI 10.1007/BF03321842 | MR 3058521 | Zbl 1283.30064
[3] Banerjee, A., Maity, S.: On the extended class of SUPM and their generating URSM over non-Archimedean field. $p$-Adic Numbers Ultrametric Anal. Appl. 13 (2021), 175-185. DOI 10.1134/S2070046621030018 | MR 4308345 | Zbl 1483.30088
[4] Chen, S., Lin, W.: On uniqueness of meromorphic functions with shared-sets in an angular domain. Acta Math. Sci., Ser. B, Engl. Ed. 31 (2011), 194-206. DOI 10.1016/S0252-9602(11)60220-8 | MR 2807477 | Zbl 1240.30150
[5] Frank, G., Reinders, M.: A unique range set for meromorphic functions with 11 elements. Complex Variables, Theory Appl. 37 (1998), 185-193. DOI 10.1080/17476939808815132 | MR 1687880 | Zbl 1054.30519
[6] Fujimoto, H.: On uniqueness of meromorphic functions sharing finite sets. Am. J. Math. 122 (2000), 1175-1203. DOI 10.1353/ajm.2000.0045 | MR 1797660 | Zbl 0983.30013
[7] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions. Nagoya Math. J. 161 (2001), 193-206. DOI 10.1017/S0027763000027215 | MR 1820218 | Zbl 0981.30023
[8] Lahiri, I.: 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
[9] Langley, J. K.: An application of the Tsuji characteristic. J. Fac. Sci., Univ. Tokyo, Sect. I A 38 (1991), 299-318. MR 1127084 | Zbl 0747.30021
[10] Lin, W., Mori, S., Tohge, K.: Uniqueness theorems in an angular domain. Tohoku Math. J. (2) 58 (2006), 509-527. DOI 10.2748/tmj/1170347687 | MR 2297197 | Zbl 1134.30026
[11] Lin, W., Mori, S., Yi, H. X.: Uniqueness theorems of entire functions with shared-set in an angular domain. Acta Math. Sin., Engl. Ser. 24 (2008), 1925-1934. DOI 10.1007/s10114-008-5479-y | MR 2453072 | Zbl 1163.30017
[12] Rathod, A.: The shared set and uniqueness of meromorphic functions in an angular domain. Tbil. Math. J. 14 (2021), 95-109. DOI 10.32513/tmj/19322008145 | MR 4307901 | Zbl 07534904
[13] Wu, Z.-J., Sun, D.-C.: A remark on uniqueness theorems in an angular domain. Proc. Japan Acad., Ser. A 84 (2008), 73-77. DOI 10.3792/pjaa.84.73 | MR 2422733 | Zbl 1157.30024
[14] Xu, H.-Y., Cao, T.-B.: Uniqueness of meromorphic functions sharing four values $IM$ and one set in an angular domain. Bull. Belg. Math. Soc. - Simon Stevin 17 (2010), 937-948. DOI 10.36045/bbms/1292334068 | MR 2777783 | Zbl 1206.30044
[15] Xu, H.-Y., Xuan, Z.-X., Wang, H.: The unique range set of meromorphic functions in an angular domain. Sci. World J. 2014 (2014), Article ID 564640, 10 pages. DOI 10.1155/2014/564640
[16] Zheng, J.-H.: On uniqueness of meromorphic functions with shared values in some angular domains. Can. Math. Bull. 47 (2004), 152-160. DOI 10.4153/CMB-2004-016-1 | MR 2032277 | Zbl 1045.30019
[17] Zheng, J.: Value Distribution of Meromorphic Functions. Springer, Berlin (2010). DOI 10.1007/978-3-642-12909-4 | MR 2757285 | Zbl 1233.30004
Search
Partner of
