Fixed point methods for a certain class of operators
Alfredo Iusem | Gárciga, Rolando
fixed point | approximate solutions | hypomonotone operators | semimonotone operators | proximal point algorithm
We introduce a new class of nonlinear operators which contains, among others, the class of operators with semimonotone additive inverse and also the class of nonexpansive mappings. We study this class ans establish some of its properties. Then we present iterative procedures for finding fixed points of operators in this class, which allow for inexact solution of the subproblems and relative error criteria. We prove weak convergence of the generated sequence in the context of Hilbert spaces. Strong convergence is also discussed.