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Power of meromorphic function sharing polynomials with derivative of it’s combination with it’s shift

  • Sujoy Majumder EMAIL logo und Somnath Saha
Veröffentlicht/Copyright: 5. Oktober 2019
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Abstract

In this paper we consider the situation when a power of a transcendental meromorphic function shares non-zero polynomials with derivative of it’s combination with it’s shift. Also we exhibit some examples to fortify the conditions of our results.

MSC 2010: 30D35
  1. (Communicated by Stanisława Kanas)

References

[1] Chiang, Y. M.—Feng, S. J.: On the Nevanlinna characteristic f(z + η) and difference equations in complex plane, Ramanujan J. 16 (2008), 105–129.10.1007/s11139-007-9101-1Suche in Google Scholar

[2] Clunie, J.: On integral and meromorphic functions, J. London Math. Soc. 37 (1962), 17–22.10.1112/jlms/s1-37.1.17Suche in Google Scholar

[3] Gundersen, G. G.: Meromorphic functions that share two finite values with their derivative, Pacific J. Math. 105 (1983), 299–309.10.2140/pjm.1983.105.299Suche in Google Scholar

[4] Hayman, W. K.: Meromorphic Functions, Clarendon Press, Oxford (1964).Suche in Google Scholar

[5] Laine, I.: Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, 1993.10.1515/9783110863147Suche in Google Scholar

[6] Lü, F.—Yi, H. X.: The Brück conjecture and entire functions sharing polynomials with their k-th derivatives, J. Korean Math. Soc. 48(3) (2011), 499–512.10.4134/JKMS.2011.48.3.499Suche in Google Scholar

[7] Lü, W.—Li, Q.—Yang, C.: On the transcendental entire solutions of a class of differential equations, Bull. Korean Math. Soc. 51(5) (2014), 1281–1289.10.4134/BKMS.2014.51.5.1281Suche in Google Scholar

[8] Majumder, S.: A Result On A Conjecture of W. Lü, Q. Li and C. Yang, Bull. Korean Math. Soc. 53(2) (2016), 411–421.10.4134/BKMS.2016.53.2.411Suche in Google Scholar

[9] Mues, E.—Steinmetz, N.: Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), 195–206.10.1007/BF01303627Suche in Google Scholar

[10] Rubel, L. A.—Yang, C. C.: Values shared by an entire function and its derivative, Lecture Notes in Math. 599, Springer-Verlag, Berlin, 1977, pp. 101–103.10.1007/BFb0096830Suche in Google Scholar

[11] Yang, L. Z.: Entire functions that share finite values with their derivatives, Bull. Austral. Math. Soc. 41 (1990), 337–342.10.1017/S0004972700018190Suche in Google Scholar

[12] Yang, C. C.: On Deficiencies of Differential Polynomials, II, Math. Z. 125 (1972), 107–112.10.1007/BF01110921Suche in Google Scholar

[13] Yang, L. Z.—Zhang, J. L.: Non-existence of meromorphic solutions of Fermat type functional equation, Aequations Math. 76(1–2) (2008), 140–150.10.1007/s00010-007-2913-7Suche in Google Scholar

[14] Yang, C. C.—Yi, H. X.: Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.10.1007/978-94-017-3626-8Suche in Google Scholar

[15] Zhang, J. L.: Meromorphic functions sharing a small function with their derivatives, Kyungpook Math. J. 49 (2009), 143–154.10.5666/KMJ.2009.49.1.143Suche in Google Scholar

[16] Zhang, J. L.—Yang, L. Z.: A power of a meromorphic function sharing a small function with its derivative, Annales Academiæ Scientiarum Fennicæ Mathematica 34 (2009), 249–260.Suche in Google Scholar

[17] Zhang, J. L.—Yang, L. Z.: A power of an entire function sharing one value with its derivative, Comput. Math. Appl. 60 (2010), 2153–2160.10.1016/j.camwa.2010.08.001Suche in Google Scholar

Received: 2018-08-04
Accepted: 2018-12-04
Published Online: 2019-10-05
Published in Print: 2019-10-25

© 2019 Mathematical Institute Slovak Academy of Sciences

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