On Certain Fermat Diophantine Functional Equations C2

In this paper, we study entire solutions and meromorphic solutions of the following Fermat Diophantine functional equations h (z(1), z(2)) f + k (z(1), z(2)) g(n) = 1 in C-2 for integers n >= 2, where h (z(1), z(2)) and k (z(1), z(2)) are non-zero meromorphic functions in C-2, and show that f and g can reduce to a constant or rational function under the conditions that (kg(n))(z1) not equivalent to 0 , L((hf)(z2)) subset of L((kg(n))(z1)/(kg(n-1))) and L(f) subset of L((kg(n))(z1)/(kg(n-1))) ignoring multiplicities or counting multiplicities.