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On the approximative roots of maximal monotone mappings. (English) Zbl 0851.65043
For the generalized equation $$Tz\ni 0$$, where $$T$$ is a monotone point-to-set mapping, the case is studied when this equation has no solution. For this problem the notion of approximative roots is introduced. Existence theorems are proved and numerical methods for finding approximate solutions are proposed.

##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
##### Keywords:
maximal monotone mappings; approximative roots