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 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Naveenkumar S. H.  1; Chaithra C. N. 2; Jayarama H. R.2
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| 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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