Nonlinear differential polynomials sharing a non-zero polynomial with finite weight

Abhijit Banerjee; Molla Basir AHAMED

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 1, page 13-36
  • ISSN: 0862-7959

Abstract

top
In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely h n ( h - 1 ) m ( h = f , g ), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of the sharing non-zero polynomial or when the first derivative is taken under consideration, better conclusions can be obtained.

How to cite

top

Banerjee, Abhijit, and AHAMED, Molla Basir. "Nonlinear differential polynomials sharing a non-zero polynomial with finite weight." Mathematica Bohemica 141.1 (2016): 13-36. <http://eudml.org/doc/276810>.

@article{Banerjee2016,
abstract = {In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely $h^\{n\}(h-1)^\{m\}$ ($h=f,g$), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of the sharing non-zero polynomial or when the first derivative is taken under consideration, better conclusions can be obtained.},
author = {Banerjee, Abhijit, AHAMED, Molla Basir},
journal = {Mathematica Bohemica},
keywords = {uniqueness; meromorphic function; nonlinear differential polynomial},
language = {eng},
number = {1},
pages = {13-36},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonlinear differential polynomials sharing a non-zero polynomial with finite weight},
url = {http://eudml.org/doc/276810},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Banerjee, Abhijit
AU - AHAMED, Molla Basir
TI - Nonlinear differential polynomials sharing a non-zero polynomial with finite weight
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 1
SP - 13
EP - 36
AB - In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely $h^{n}(h-1)^{m}$ ($h=f,g$), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of the sharing non-zero polynomial or when the first derivative is taken under consideration, better conclusions can be obtained.
LA - eng
KW - uniqueness; meromorphic function; nonlinear differential polynomial
UR - http://eudml.org/doc/276810
ER -

References

top
  1. Alzahary, T. C., Yi, H. X., 10.1080/02781070410001701074, Complex Variables, Theory Appl. 49 (2004), 1063-1078. (2004) Zbl1067.30055MR2111304DOI10.1080/02781070410001701074
  2. Banerjee, A., 10.32917/hmj/1200529810, Hiroshima Math. J. 37 (2007), 397-408. (2007) Zbl1152.30023MR2376726DOI10.32917/hmj/1200529810
  3. Banerjee, A., 10.4064/ap89-3-3, Ann. Pol. Math. 89 (2006), 259-272. (2006) Zbl1104.30018MR2262553DOI10.4064/ap89-3-3
  4. Banerjee, A., 10.1155/IJMMS.2005.3587, Int. J. Math. Math. Sci. 2005 (2005), 3587-3598. (2005) Zbl1093.30024MR2205158DOI10.1155/IJMMS.2005.3587
  5. Fang, M., Qiu, H., 10.1006/jmaa.2000.7270, J. Math. Anal. Appl. 268 (2002), 426-439. (2002) Zbl1030.30028MR1896207DOI10.1006/jmaa.2000.7270
  6. Frank, G., Eine Vermutung von Hayman über Nullstellen meromorpher Funktionen, Math. Z. 149 German (1976), 29-36. (1976) MR0422615
  7. Hayman, W. K., Meromorphic Functions, Oxford Mathematical Monographs Clarendon Press, Oxford (1964). (1964) Zbl0115.06203MR0164038
  8. Lahiri, I., On a question of Hong Xun Yi, Arch. Math., Brno 38 (2002), 119-128. (2002) Zbl1087.30028MR1909593
  9. Lahiri, I., 10.1017/S0027763000027215, Nagoya Math. J. 161 (2001), 193-206. (2001) Zbl0981.30023MR1820218DOI10.1017/S0027763000027215
  10. Lahiri, I., 10.1080/17476930108815411, Complex Variables, Theory Appl. 46 (2001), 241-253. (2001) Zbl1025.30027MR1869738DOI10.1080/17476930108815411
  11. Lahiri, I., 10.4064/ap-71-2-113-128, Ann. Pol. Math. 71 (1999), 113-128. (1999) Zbl0938.30022MR1703886DOI10.4064/ap-71-2-113-128
  12. Lahiri, I., Dewan, S., 10.2996/kmj/1050496651, Kodai Math. J. 26 (2003), 95-100. (2003) Zbl1077.30025MR1966685DOI10.2996/kmj/1050496651
  13. Lahiri, I., Mandal, N., 10.1155/IJMMS.2005.1933, Int. J. Math. Math. Sci. 2005 (2005), 1933-1942. (2005) Zbl1084.30029MR2176445DOI10.1155/IJMMS.2005.1933
  14. Lahiri, I., Pal, R., 10.4134/BKMS.2006.43.1.161, Bull. Korean Math. Soc. 43 (2006), 161-168. (2006) MR2204868DOI10.4134/BKMS.2006.43.1.161
  15. Lahiri, I., Sahoo, P., Uniqueness of non-linear differential polynomials sharing 1-points, Georgian Math. J. 12 (2005), 131-138. (2005) Zbl1073.30022MR2136891
  16. Lahiri, I., Sarkar, A., Nonlinear differential polynomials sharing 1-points with weight two, Chin. J. Contemp. Math. 25 (2004), 325-334. (2004) Zbl1069.30051MR2159311
  17. Li, X.-M., Gao, L., 10.4134/BKMS.2010.47.2.319, Bull. Korean Math. Soc. 47 (2010), 319-339. (2010) Zbl1189.30066MR2650701DOI10.4134/BKMS.2010.47.2.319
  18. Lin, W. C., Uniqueness of differential polynomials and a problem of Lahiri, Pure Appl. Math. 17 Chinese (2001), 104-110. (2001) MR1848848
  19. Lin, W.-C., Yi, H.-X., Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math. 35 (2004), 121-132. (2004) Zbl1056.30031MR2040726
  20. Meng, C., 10.32917/hmj/1249046335, Hiroshima Math. J. 39 (2009), 163-179. (2009) Zbl1182.30051MR2543648DOI10.32917/hmj/1249046335
  21. Qiu, H., Fang, M., 10.4134/BKMS.2004.41.1.109, Bull. Korean Math. Soc. 41 (2004), 109-116. (2004) Zbl1134.30325MR2036806DOI10.4134/BKMS.2004.41.1.109
  22. Sahoo, P., 10.5666/KMJ.2013.53.2.191, Kyungpook Math. J. 53 (2013), 191-205. (2013) MR3078082DOI10.5666/KMJ.2013.53.2.191
  23. Sahoo, P., Uniqueness of meromorphic functions when two differential polynomials share one value , Mat. Vesn. 62 (2010), 169-182. (2010) Zbl1289.30190MR2639145
  24. Yamanoi, K., 10.1007/BF02392741, Acta Math. 192 (2004), 225-294. (2004) Zbl1203.30035MR2096455DOI10.1007/BF02392741
  25. Yang, C.-C., Hua, X., Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn., Math. 22 (1997), 395-406. (1997) Zbl0890.30019MR1469799
  26. Yang, C.-C., Yi, H.-X., Uniqueness Theory of Meromorphic Functions, Mathematics and Its Applications 557 Kluwer Academic Publishers, Dordrecht; Science Press, Beijing (2003). (2003) Zbl1070.30011MR2105668
  27. Yi, H. X., On characteristic function of a meromorphic function and its derivative, Indian J. Math. 33 (1991), 119-133. (1991) Zbl0799.30018MR1140875
  28. Zhang, Q., Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. (electronic only) 6 (2005), Article No. 116, 13 pages. (2005) Zbl1097.30033MR2178297

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.