A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value

  • A. Banerjee University of Kalyani, West Bengal, India
  • A. Roy University of Kalyani, West Bengal, India
Keywords: Meromorphic function, small function, uniqueness, linear shift delay differential operator, hyper-order.

Abstract

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing a small function together with a value which improve and complement some earlier results. In particular, more or less we have improved and extended two results of Qi-Yang [Meromorphic functions that share values with their shifts or their $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling the superfluous conclusions in them.

Author Biographies

A. Banerjee, University of Kalyani, West Bengal, India

Associate Professor, Department of Mathematics, University of Kalyani, West Bengal, India

A. Roy, University of Kalyani, West Bengal, India

Department of Mathematics, University of Kalyani, West Bengal, India

References

Chen Z.X., On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations, Sci. China Math., 54 (2011), 2123–2133.

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.

Halburd R.G., Korhonen R.J., Tohge K., Holomorphic curves with shift invariant hyperplane preimages, Trans. Amer. Math. Soc., 366 (2014), 4267–4298.

Hayman W.K., Meromorphic Functions, The Clarendon Press, Oxford, 1964.

Liu K., Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl., 359 (2009), 384–393.

Lu F., Han Q., On the Fermat-type equation f3(z)+f3f(z +c) = 1, Aequationes Math., 91 (2017), №1, 129–136.

Qi X.G., Yang L.Z., Liu K., Uniqueness and periodicity of meromorphic functions concerning difference operator, Comput. Math. Appl., 60 (2010), 1739–1746.

Qi X.G., Dou J., Yang L.Z., Uniqueness and value distribution for difference operators of meromorphic function, Adv. Differ. Equ., 32 (2012) , 1–9.

Qi X.G., Yang L.Z., Meromorphic functions that share values with their shifts or their n-th order differences, Analysis Math., 46 (2020), №4, 843–865.

Yang L., Value distribution theory, Springer, New York, 1993.

Yang C.C., Yi H.X., Uniqueness theory of meromorphic functions, Kluwer Academic, Dordrecht, 2003.

Published
2021-03-04
How to Cite
Banerjee, A., & Roy, A. (2021). A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value. Matematychni Studii, 55(1), 57-63. https://doi.org/10.30970/ms.55.1.57-63
Section
Articles