The iterative solution of the equation
for a monotone operator T in
spaces. (English) Zbl 0606.47067
Suppose T is a multivalued monotone operator (not necessarily continuous) with open domain D(T) in , and the equation has a solution . Then there exists a neighbourhood of q and a real number such that for any , for any initial guess , and any single-valued section of T, the sequence generated from by remains in D(T) and converges strongly to q with . Furthermore, for , , measure and , suppose T is a single-valued locally Lipschitzian monotone operator with open domain D(T) in X. For , a solution of the equation is obtained as the limit of an iteratively constructed sequence with an explicit error estimate.
|47J25||Iterative procedures (nonlinear operator equations)|
|47H06||Accretive operators, dissipative operators, etc. (nonlinear)|
|65J15||Equations with nonlinear operators (numerical methods)|