# 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
• 54 3

#### Abstract

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 [1], [4] 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 [6], [8]. For example Bruck [2] obtained the iterative solution of the above equation with an explicit error estimate as follows.