Geodesic
Entire function sharing two polynomials with its $k$th derivative
Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 87-103
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We investigate the uniqueness problem of entire functions that share two polynomials with their $k$th derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible.
We investigate the uniqueness problem of entire functions that share two polynomials with their $k$th derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible.
DOI : 10.21136/MB.2023.0017-22
Classification : 30D35, 30D45
Keywords: meromorphic function; derivative; Nevanlinna theory; uniqueness 
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Majumder, Sujoy; Sarkar, Nabadwip. Entire function sharing two polynomials with its $k$th derivative. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 87-103. doi: 10.21136/MB.2023.0017-22

[1] Brück, R.: On entire functions which share one value CM with their first derivative. Result. Math. 30 (1996), 21-24. | DOI | MR | JFM

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

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

[4] Laine, I.: Nevanlinna Theory and Complex Differential Equations. de Gruyter Studies in Mathematics 15. Walter de Gruyter, Berlin (1993). | DOI | MR | JFM

[5] Li, J., Yi, H.: Normal families and uniqueness of entire functions and their derivatives. Arch. Math. 87 (2006), 52-59. | DOI | MR | JFM

[6] Lü, F., Xu, J., Chen, A.: Entire functions sharing polynomials with their first derivatives. Arch. Math. 92 (2009), 593-601. | DOI | MR | JFM

[7] Lü, F., Yi, H.: The Brück conjecture and entire functions sharing polynomials with their $k$-th derivatives. J. Korean Math. Soc. 48 (2011), 499-512. | DOI | MR | JFM

[8] Mues, E., Steinmetz, N.: Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen. Manuscr. Math. 29 (1979), 195-206 German. | DOI | MR | JFM

[9] Rubel, L. A., Yang, C.-C.: Values shared by an entire function and its derivative. Complex Analysis Lecture Notes in Mathematics 599. Springer, Berlin (1977), 101-103. | DOI | MR | JFM

[10] Schiff, J. L.: Normal Families. Universitext. Springer, New York (1993). | DOI | MR | JFM

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

[12] Yang, L.-Z., Zhang, J.-L.: Non-existence of meromorphic solutions of Fermat type functional equation. Aequationes Math. 76 (2008), 140-150. | DOI | MR | JFM

[13] Zhang, J.-L., Yang, L.-Z.: A power of an entire function sharing one value with its derivative. Comput. Math. Appl. 60 (2010), 2153-2160. | DOI | MR | JFM

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