On a result of Zhang and Xu concerning their open problem

Sujoy Majumder; Rajib Mandal

Archivum Mathematicum (2018)

  • Volume: 054, Issue: 2, page 65-89
  • ISSN: 0044-8753

Abstract

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The motivation of this paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial with the help of the idea of normal family. The result of the paper improves and generalizes the recent result due to Zhang and Xu [24]. Our another remarkable aim is to solve an open problem as posed in the last section of [24].

How to cite

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Majumder, Sujoy, and Mandal, Rajib. "On a result of Zhang and Xu concerning their open problem." Archivum Mathematicum 054.2 (2018): 65-89. <http://eudml.org/doc/294458>.

@article{Majumder2018,
abstract = {The motivation of this paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial with the help of the idea of normal family. The result of the paper improves and generalizes the recent result due to Zhang and Xu [24]. Our another remarkable aim is to solve an open problem as posed in the last section of [24].},
author = {Majumder, Sujoy, Mandal, Rajib},
journal = {Archivum Mathematicum},
keywords = {normal families; uniqueness; meromorphic function; small functions},
language = {eng},
number = {2},
pages = {65-89},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On a result of Zhang and Xu concerning their open problem},
url = {http://eudml.org/doc/294458},
volume = {054},
year = {2018},
}

TY - JOUR
AU - Majumder, Sujoy
AU - Mandal, Rajib
TI - On a result of Zhang and Xu concerning their open problem
JO - Archivum Mathematicum
PY - 2018
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 054
IS - 2
SP - 65
EP - 89
AB - The motivation of this paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial with the help of the idea of normal family. The result of the paper improves and generalizes the recent result due to Zhang and Xu [24]. Our another remarkable aim is to solve an open problem as posed in the last section of [24].
LA - eng
KW - normal families; uniqueness; meromorphic function; small functions
UR - http://eudml.org/doc/294458
ER -

References

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  1. Banerjee, A., 10.1016/j.jmaa.2006.04.078, J. Math. Anal. Appl. 327 (2) (2007), 1273–1283. (2007) Zbl1115.30029MR2280003DOI10.1016/j.jmaa.2006.04.078
  2. Banerjee, A., 10.5666/KMJ.2011.51.1.043, Kyungpook Math. J. 51 (2011), 43–58. (2011) MR2784645DOI10.5666/KMJ.2011.51.1.043
  3. Chang, J.M., Zalcman, L., 10.1016/j.jmaa.2007.05.079, J. Math. Anal. Appl. 338 (2008), 1191–1205. (2008) MR2386477DOI10.1016/j.jmaa.2007.05.079
  4. Fang, M.L., Qiu, H.L., 10.1006/jmaa.2000.7270, J. Math. Anal. Appl. 268 (2002), 426–439. (2002) Zbl1030.30028MR1896207DOI10.1006/jmaa.2000.7270
  5. Frank, G., 10.1007/BF01301627, Math. Z. 149 (1976), 29–36. (1976) DOI10.1007/BF01301627
  6. Hayman, W.K., Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959). (1959) Zbl0088.28505
  7. Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford, 1964. (1964) Zbl0115.06203
  8. Lahir, I., Banerjee, A., Weighted sharing of two sets, Kyungpook Math. J. 46 (2006). (2006) MR2214802
  9. Lahiri, I., 10.1155/S0161171201011036, Internat. J. Math. Math. Sci. 28 (2001), 83–91. (2001) Zbl0999.30023MR1885054DOI10.1155/S0161171201011036
  10. Lahiri, I., 10.1017/S0027763000027215, Nagoya Math. J. 161 (2001), 193–206. (2001) Zbl0981.30023MR1820218DOI10.1017/S0027763000027215
  11. Lahiri, I., 10.1080/17476930108815411, Complex Variables Theory Appl. 46 (2001), 241–253. (2001) Zbl1025.30027MR1869738DOI10.1080/17476930108815411
  12. Lahiri, I., Dewan, S., 10.2996/kmj/1050496651, Kodai Math. J. 26 (2003), 95–100. (2003) Zbl1077.30025MR1966685DOI10.2996/kmj/1050496651
  13. Majumder, S., On an open problem of Xiao-Bin Zhang and Jun-Feng Xu, Demonstratio Math. 49 (2) (2016), 161–182. (2016) MR3507931
  14. Pang, X.C., Normality conditions for differential polynomials, Kexue Tongbao (Chinese) 33 (1988), 1690–1693. (1988) 
  15. Schiff, J., Normal families, Berlin, 1993. (1993) 
  16. Xu, J.F., Lü, F., Yi, H.X., 10.1016/j.camwa.2009.07.024, Comput. Math. Appl. 59 (2010), 9–17. (2010) MR2575487DOI10.1016/j.camwa.2009.07.024
  17. Yamanoi, K., 10.1007/BF02392741, Acta Math. 192 (2004), 225–294. (2004) Zbl1203.30035MR2096455DOI10.1007/BF02392741
  18. Yang, C.C., 10.1007/BF01110921, Math. Z. 125 (1972), 107–112. (1972) Zbl0217.38402DOI10.1007/BF01110921
  19. Yang, C.C., Hua, X.H., Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395–406. (1997) Zbl0890.30019
  20. Yang, C.C., Yi, H.X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003. (2003) Zbl1070.30011MR2105668
  21. Zalcman, L., 10.1080/00029890.1975.11993942, Amer. Math. Monthly 82 (1975), 813–817. (1975) DOI10.1080/00029890.1975.11993942
  22. Zalcman, L., 10.1090/S0273-0979-98-00755-1, Bull. Amer. Math. Soc. 35 (1998), 215–230. (1998) DOI10.1090/S0273-0979-98-00755-1
  23. Zhang, Q.C., Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (4) (2005), Art.116 online http://jipam.vu.edu.au/. (2005) Zbl1097.30033MR2178297
  24. Zhang, X.B., Xu, J.F., 10.1016/j.camwa.2010.12.022, Comput. Math. Appl. 61 (2011), 722–730. (2011) MR2764068DOI10.1016/j.camwa.2010.12.022

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