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

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) bea transcendental meromorphic function with finite order m, n and k be a positive integers such thatm ≥ (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.