International Journal of Nonlinear Analysis and Applications

Nevanlinna's counting functions for difference operators and related results

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Rd, Ballygunge, Kolkata-700019, West Bengal, India

2 Department of Mathematics, Bethune College, 181, Bidhan Sarani, Manicktala, Azad Hind Bag, Kolkata-700006, West Bengal, India

Abstract

The study of the Nevanlinna theory for difference operators was introduced independently by Halburd & Korhonen and Chiang & Feng in the years 2006 and 2008 respectively. Halburd and Korhonen proved the uniqueness theorem for meromorphic functions associated with c-separated pairs. In this paper, we have generalised the result by introducing c-separated pairs of multiplicity p and their counting functions. We have deduced some analogues of certain unique results of classical Nevanlinna theory due to Chen, Chen & Tsai; Gopalakrishna & Bhoosnurmath; and Lahiri & Pal. Thereafter, we have also discussed certain implications of the deduced results.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 12
December 2023
Pages 359-371
  • Receive Date: 11 July 2022
  • Revise Date: 16 March 2023
  • Accept Date: 23 March 2023