ON THE TRANSCENDENTAL SOLUTION OF THE FERMAT TYPE Q-SHIFT EQUATION

S. H., Naveenkumar; C. N., Chaithra; H. R., Jayarama

doi:10.21608/ejmaa.2023.191325.1001

	ON THE TRANSCENDENTAL SOLUTION OF THE FERMAT TYPE Q-SHIFT EQUATION
Electronic Journal of Mathematical Analysis and Applications
Volume 11, Issue 2, July 2023, Page 1-6 PDF (459.96 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2023.191325.1001
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Authors
Naveenkumar S. H. ¹; Chaithra C. N. ²; Jayarama H. R.²
¹Presidency University, Yelahanka Bangalore-560064
²Presidency University Itgalpura Yelahanka
Abstract
In Nevanlinna’s value distribution theory we considering some basic terms like T(r, f), N(r, f), m(r, f) etc., and let fm(z) + q(z)[fn∆qηf](k) = p(z) be a non-linear q-th order difference equation and f(z) be a transcendental meromorphic function with finite order m, n and k be a positive integers such that m ≥ (q + 1)(nk + k + 2) + 3, p(z) be a meromorphic function satisfying N r, p(1z) = S(r, f). The q(z) be a non-zero meromorphic function satisfying that T(r, q(z)) = S(r, f), then f(z) is not a solution of the non-linear q-th order difference equation. In this paper, we mainly investigate the uniqueness result of transcendental Fermat type q-shift equation by considering q-th order difference equation. Our result improves the results due to Abhijit Banerjee and Tania Biswas. In addition to that the example is exhibited to validate certain claims and justification of our main result.
Keywords
Nevanlinna theory; Difference polynomial of difference operator; Finite order; Entire and Meromorphic solutions


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