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Generalized KM theorems and their applications. (English) Zbl 1117.65081

The authors consider several generalizations of classical Krasnnoselski-Mann (KM) iterations. Under suitable condicition, some generalized KM theorems are proved. As applications, some iterative algorithms to find zero points of maximal monotone operators and to solve variational inequalities are obtained.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
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