Geometric estimation of the solution to π₯+ππ₯=0 for unbounded densely defined monotone operator π in Hilbert space
T. E. Williamson Β· Proceedings of the American Mathematical Society Β· 1979
In recent papers R. Bruck and J. C. Dunn have given convergent schemes for approximating the solution p of x + T x = f x + Tx = f for T a monotone mapping on a Hilbert space, with T locally bounded. The present paper derives a geometric fact and uses this in a direct manner to give a scheme applicable to densely defined T . The scheme is computable with decreasing error estimates without any assumptions of boundedness. The convergence of the scheme to the solution p is proven under the weak condition that β x n + T x n β \left \| {{x_n} + T{x_n}} \right \| grow no faster than n 1 / 2 {n^{1/2}} .