Dieter Schott
Weak convergence of iterative methods generated by strongly Fejer monotone mappings
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 51, 83-96 (1997)
65J05 General theory
47H04 Set-valued operators, See also {28B20, 54C60, 58C06}
47H09 Nonexpansive mappings, and their generalizations
Abstract: We consider the general class of strongly
Fej\'{e}r monotone mappings and the subclass of strongly nonexpansive
operators. We show that only a few additional assumptions suffice to
obtain weak convergence of the corresponding iterative methods.
These methods can be widely used to solve convex problems. Besides,
we get generalizations of convergence results known from the literature.
Keywords: Set-valued mappings, Fej\'{e}r monotone mappings, nonexpansive operators, relaxations, convex problems, Fej\'{e}r monotone sequences, iterative methods