Geodesic
On the generalization of two results of Cao and Zhang
Mathematica Bohemica, Tome 142 (2017) no. 4, pp. 357-380
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper studies the uniqueness of meromorphic functions $$f^{n}\prod _{i=1}^{k}(f^{(i)})^{n_{i}}\quad \mbox {and}\quad g^{n}\prod _{i=1}^{k}(g^{(i)})^{n_{i}}$$ that share two values, where $n, n_{k}, k\in \mathbb {N}$, $n_{i}\in \mathbb {N}\cup \{0\}$, $i=1,2,\ldots ,k-1$. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
This paper studies the uniqueness of meromorphic functions $$f^{n}\prod _{i=1}^{k}(f^{(i)})^{n_{i}}\quad \mbox {and}\quad g^{n}\prod _{i=1}^{k}(g^{(i)})^{n_{i}}$$ that share two values, where $n, n_{k}, k\in \mathbb {N}$, $n_{i}\in \mathbb {N}\cup \{0\}$, $i=1,2,\ldots ,k-1$. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
DOI : 10.21136/MB.2017.0021-15
Classification : 30D35
Keywords: uniqueness; meromorphic function; weighted sharing; nonlinear differential polynomials 
@article{10_21136_MB_2017_0021_15,
     author = {Majumder, Sujoy},
     title = {On the generalization of two results of {Cao} and {Zhang}},
     journal = {Mathematica Bohemica},
     pages = {357--380},
     year = {2017},
     volume = {142},
     number = {4},
     doi = {10.21136/MB.2017.0021-15},
     mrnumber = {3739023},
     zbl = {06819591},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0021-15/}
}
TY  - JOUR
AU  - Majumder, Sujoy
TI  - On the generalization of two results of Cao and Zhang
JO  - Mathematica Bohemica
PY  - 2017
SP  - 357
EP  - 380
VL  - 142
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0021-15/
DO  - 10.21136/MB.2017.0021-15
LA  - en
ID  - 10_21136_MB_2017_0021_15
ER  - 
%0 Journal Article
%A Majumder, Sujoy
%T On the generalization of two results of Cao and Zhang
%J Mathematica Bohemica
%D 2017
%P 357-380
%V 142
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0021-15/
%R 10.21136/MB.2017.0021-15
%G en
%F 10_21136_MB_2017_0021_15
Majumder, Sujoy. On the generalization of two results of Cao and Zhang. Mathematica Bohemica, Tome 142 (2017) no. 4, pp. 357-380. doi: 10.21136/MB.2017.0021-15

[1] Banerjee, A.: On a question of Gross. J. Math. Anal. Appl. 327 (2007), 1273-1283. | DOI | MR | JFM

[2] Bergweiler, W., Eremenko, A.: On the singularities of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoam. 11 (1995), 355-373. | DOI | MR | JFM

[3] Cao, Y.-H., Zhang, X.-B.: Uniqueness of meromorphic functions sharing two values. J. Inequal. Appl. (electronic only) 2012 (2012), Article ID 100, 10 pages. | DOI | MR | JFM

[4] Chen, H. H., Fang, M. L.: The value distribution of $f^{n}f'$. Sci. China Ser. A. 38 (1995), 789-798. | DOI | MR | JFM

[5] Fang, M., Hua, X.: Entire functions that share one value. J. Nanjing Univ., Math. Biq. 13 (1996), 44-48. | MR | JFM

[6] Fang, M., Qiu, H.: Meromorphic functions that share fixed-points. J. Math. Anal. Appl. 268 (2002), 426-439. | DOI | MR | JFM

[7] Frank, G.: Eine Vermutung von Hayman über Nullstellen meromorpher Funktionen. Math. Z. 149 (1976), 29-36. | DOI | MR | JFM

[8] Hayman, W. K.: Meromorphic functions. Oxford Mathematical Monographs. Clarendon Press, Oxford (1964). | MR | JFM

[9] Köhler, L.: Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros. Complex Variables, Theory Appl. 11 (1989), 39-48. | DOI | MR | JFM

[10] Lahiri, I.: Weighted value sharing and uniqueness of meromorphic functions. Complex Variables, Theory Appl. 46 (2001), 241-253. | DOI | MR | JFM

[11] Lahiri, I., Dewan, S.: Value distribution of the product of a meromorphic function and its derivative. Kodai Math. J. 26 (2003), 95-100. | DOI | MR | JFM

[12] Lahiri, I., Sarkar, A.: Nonlinear differential polynomials sharing 1-points with weight two. Chin. J. Contemp. Math. 25 (2004), 325-334. | MR | JFM

[13] Xu, J., Yi, H., Zhang, Z.: Some inequalities of differential polynomials. Math. Inequal. Appl. 12 (2009), 99-113. | DOI | MR | JFM

[14] Yamanoi, K.: The second main theorem for small functions and related problems. Acta Math. 192 (2004), 225-294. | DOI | MR | JFM

[15] Yang, C. C.: On deficiencies of differential polynomials II. Math. Z. 125 (1972), 107-112. | DOI | MR | JFM

[16] Yang, C.-C., Hua, X.: Uniqueness and value-sharing of meromorphic functions. Ann. Acad. Sci. Fenn., Math. 22 (1997), 395-406. | MR | JFM

[17] Yang, C. C., Yi, H. X.: Uniqueness Theory of Meromorphic Functions. Mathematics and its Applications 557. Kluwer Academic Publishers, Dordrecht (2003). | DOI | MR | JFM

[18] Yang, L.: Value Distribution Theory. Springer, Berlin; Science Press, Beijing (1993). | DOI | MR | JFM

[19] Yi, H. X.: On characteristic function of a meromorphic function and its derivative. Indian J. Math. 33 (1991), 119-133. | MR | JFM

[20] Zhang, Q.: Meromorphic function that shares one small function with its derivative. \mbox{JIPAM}, J. Inequal. Pure Appl. Math. (electronic only) 6 (2005), Article No. 116, 13 pages. | MR | JFM

Cité par Sources :