Uniqueness and two shared set problems of meromorphic functions in a different angle

Sanjay Mallick; Abhijit Banerjee

Mathematica Bohemica (2021)

  • Issue: 1, page 19-45
  • ISSN: 0862-7959

Abstract

top
The purpose of the paper is to represent the two shared set problems in an elaborative and convenient manner. In the main result of the paper, we have exhaustively treated the two shared set problem on the open complex plane. As a consequence of the main result, we have investigated the same problem in a different perspective, which has yet not been studied. Further, two examples have been exhibited in the paper to show the sharpness of some of these results.

How to cite

top

Mallick, Sanjay, and Banerjee, Abhijit. "Uniqueness and two shared set problems of meromorphic functions in a different angle." Mathematica Bohemica (2021): 19-45. <http://eudml.org/doc/297324>.

@article{Mallick2021,
abstract = {The purpose of the paper is to represent the two shared set problems in an elaborative and convenient manner. In the main result of the paper, we have exhaustively treated the two shared set problem on the open complex plane. As a consequence of the main result, we have investigated the same problem in a different perspective, which has yet not been studied. Further, two examples have been exhibited in the paper to show the sharpness of some of these results.},
author = {Mallick, Sanjay, Banerjee, Abhijit},
journal = {Mathematica Bohemica},
keywords = {meromorphic function; uniqueness; weighted sharing; shared set},
language = {eng},
number = {1},
pages = {19-45},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniqueness and two shared set problems of meromorphic functions in a different angle},
url = {http://eudml.org/doc/297324},
year = {2021},
}

TY - JOUR
AU - Mallick, Sanjay
AU - Banerjee, Abhijit
TI - Uniqueness and two shared set problems of meromorphic functions in a different angle
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 19
EP - 45
AB - The purpose of the paper is to represent the two shared set problems in an elaborative and convenient manner. In the main result of the paper, we have exhaustively treated the two shared set problem on the open complex plane. As a consequence of the main result, we have investigated the same problem in a different perspective, which has yet not been studied. Further, two examples have been exhibited in the paper to show the sharpness of some of these results.
LA - eng
KW - meromorphic function; uniqueness; weighted sharing; shared set
UR - http://eudml.org/doc/297324
ER -

References

top
  1. Banerjee, A., 10.4064/ap92-3-5, Ann. Pol. Math. 92 (2007), 261-274. (2007) Zbl1130.30027MR2353890DOI10.4064/ap92-3-5
  2. Banerjee, A., 10.1515/GMJ.2008.21, Georgian Math. J. 15 (2008), 21-38. (2008) Zbl1159.30018MR2418873DOI10.1515/GMJ.2008.21
  3. Banerjee, A., On the uniqueness of meromorphic functions sharing two sets, Commun. Math. Anal. 9 (2010), 1-11. (2010) Zbl1195.30042MR2737750
  4. Banerjee, A., Bi-unique range sets for meromorphic functions, Nihonkai Math. J. 24 (2013), 121-134. (2013) Zbl1291.30189MR3178503
  5. Banerjee, A., Corrigendum to ``Bi-unique range sets for meromorphic functions'', Nihonkai Math. J. 26 (2015), 71-74. (2015) Zbl06566363MR3482758
  6. Banerjee, A., Bhattacharjee, P., 10.2478/s12175-011-0005-6, Math. Slovaca 61 (2011), 197-214. (2011) Zbl1265.30141MR2786694DOI10.2478/s12175-011-0005-6
  7. Banerjee, A., Majumder, S., Mukherjee, S., A uniqueness result on meromorphic functions sharing two sets II, Fasc. Math. 53 (2014), 17-30. (2014) Zbl1331.30018MR3331510
  8. Banerjee, A., Mallick, S., 10.1007/s40315-016-0174-y, Comput. Methods Funct. Theory 17 (2017), 19-45 erratum ibid. 17 2017 page 735. (2017) Zbl1364.30035MR3620877DOI10.1007/s40315-016-0174-y
  9. Fujimoto, H., 10.1353/ajm.2000.0045, Am. J. Math. 122 (2000), 1175-1203. (2000) Zbl0983.30013MR1797660DOI10.1353/ajm.2000.0045
  10. Gross, F., 10.1007/bfb0096825, Complex Analysis. Lect. Notes Math. 599 Springer, Berlin (1977), 51-67 J. D. Buckholtz et al. (1977) Zbl0357.30007MR0450529DOI10.1007/bfb0096825
  11. Han, Q., Yi, H.-X., 10.4064/ap93-1-2, Ann. Pol. Math. 93 (2008), 17-31. (2008) Zbl1160.30016MR2383339DOI10.4064/ap93-1-2
  12. Lahiri, I., 10.1155/S0161171201011036, Int. J. Math. Math. Sci. 28 (2001), 83-91. (2001) Zbl0999.30023MR1885054DOI10.1155/S0161171201011036
  13. Lahiri, I., 10.1017/S0027763000027215, Nagoya Math. J. 161 (2001), 193-206. (2001) Zbl0981.30023MR1820218DOI10.1017/S0027763000027215
  14. Lahiri, I., 10.1080/17476930108815411, Complex Variables, Theory Appl. 46 (2001), 241-253. (2001) Zbl1025.30027MR1869738DOI10.1080/17476930108815411
  15. Lin, W.-C., Yi, H.-X., Some further results on meromorphic functions that share two sets, Kyungpook Math. J. 43 (2003), 73-85. (2003) Zbl1064.30023MR1961610
  16. Yang, C. C., 10.1007/BF01110921, Math. Z. 125 (1972), 107-112. (1972) Zbl0217.38402MR0294642DOI10.1007/BF01110921
  17. Yi, B., Li, Y., Uniqueness of meromorphic functions that share two sets with CM, Acta Math. Sin., Chin. Ser. 55 Chinese (2012), 363-368. (2012) Zbl1265.30162MR2963005
  18. Yi, H.-X., Uniqueness of meromorphic functions and question of Gross, Sci. China, Ser. A 37 (1994), 802-813. (1994) Zbl0821.30024MR1324763
  19. Yi, H.-X., Meromorphic functions that share two sets, Acta Math. Sin. 45 (2002), 75-82 Chinese. (2002) Zbl1092.30051MR1923666

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.