- Volume 9 Issue 4
MANN-ITERATION PROCESS TO THE SOLUTION OF
$y=x+Tx$ FOR AN ACDRETIVE OPERATOR T IN SOME BANACH SPACES
- Park, Jong-An
- Published : 1994.10.01
If H is a Hilbert space, then an operator $T : D(T) \subset H \to H$ is said to be monotone if $$ (x-y, Tx-Ty) \geq 0$$ for any x, y in D(T). Many authors ,  obtained the existence theorem for the equation $y = x + Tx$ for x, given an element y in H and a monotone operator T. On the other hand some iterative methods were applied to the approximations for the solution of the above equation , . For example Bruck  obtained the iterative solution of the above equation with an explicit error estimate as follows.