| Title:
|
Investigations on unique range sets of meromorphic functions in an angular domain (English) |
| Author:
|
Maity, Sayantan |
| Author:
|
Banerjee, Abhijit |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
603-615 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
angular domain |
| Keyword:
|
meromorphic function |
| Keyword:
|
unique range set |
| MSC:
|
30D35 |
| idZBL:
|
Zbl 07790606 |
| idMR:
|
MR4673840 |
| DOI:
|
10.21136/MB.2022.0183-21 |
| . |
| Date available:
|
2023-11-23T12:40:40Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151977 |
| . |
| Reference:
|
[1] Banerjee, A., Bhattacharjee, P.: Uniqueness and set sharing of derivatives of meromorphic functions.Math. Slovaca 61 (2011), 197-214. Zbl 1265.30141, MR 2786694, 10.2478/s12175-011-0005-6 |
| Reference:
|
[2] Banerjee, A., Lahiri, I.: A uniqueness polynomial generating a unique range set and vice versa.Comput. Methods Funct. Theory 12 (2012), 527-539. Zbl 1283.30064, MR 3058521, 10.1007/BF03321842 |
| Reference:
|
[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. Zbl 1483.30088, MR 4308345, 10.1134/S2070046621030018 |
| Reference:
|
[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. Zbl 1240.30150, MR 2807477, 10.1016/S0252-9602(11)60220-8 |
| Reference:
|
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| Reference:
|
[6] Fujimoto, H.: On uniqueness of meromorphic functions sharing finite sets.Am. J. Math. 122 (2000), 1175-1203. Zbl 0983.30013, MR 1797660, 10.1353/ajm.2000.0045 |
| Reference:
|
[7] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions.Nagoya Math. J. 161 (2001), 193-206. Zbl 0981.30023, MR 1820218, 10.1017/S0027763000027215 |
| Reference:
|
[8] Lahiri, I.: Weighted value sharing and uniqueness of meromorphic functions.Complex Variables, Theory Appl. 46 (2001), 241-253. Zbl 1025.30027, MR 1869738, 10.1080/17476930108815411 |
| Reference:
|
[9] Langley, J. K.: An application of the Tsuji characteristic.J. Fac. Sci., Univ. Tokyo, Sect. I A 38 (1991), 299-318. Zbl 0747.30021, MR 1127084 |
| Reference:
|
[10] Lin, W., Mori, S., Tohge, K.: Uniqueness theorems in an angular domain.Tohoku Math. J. (2) 58 (2006), 509-527. Zbl 1134.30026, MR 2297197, 10.2748/tmj/1170347687 |
| Reference:
|
[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. Zbl 1163.30017, MR 2453072, 10.1007/s10114-008-5479-y |
| Reference:
|
[12] Rathod, A.: The shared set and uniqueness of meromorphic functions in an angular domain.Tbil. Math. J. 14 (2021), 95-109. Zbl 07534904, MR 4307901, 10.32513/tmj/19322008145 |
| Reference:
|
[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. Zbl 1157.30024, MR 2422733, 10.3792/pjaa.84.73 |
| Reference:
|
[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. Zbl 1206.30044, MR 2777783, 10.36045/bbms/1292334068 |
| Reference:
|
[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. 10.1155/2014/564640 |
| Reference:
|
[16] Zheng, J.-H.: On uniqueness of meromorphic functions with shared values in some angular domains.Can. Math. Bull. 47 (2004), 152-160. Zbl 1045.30019, MR 2032277, 10.4153/CMB-2004-016-1 |
| Reference:
|
[17] Zheng, J.: Value Distribution of Meromorphic Functions.Springer, Berlin (2010). Zbl 1233.30004, MR 2757285, 10.1007/978-3-642-12909-4 |
| . |
