On the stability of the existence of fixed points for the projection-iterative methods with relaxation

Andrzej Komisarski, Adam Paszkiewicz

We consider an $\alpha$-relaxed projection $P_A^{\alpha }:H\to H$ given by $P_A^{\alpha }(x)=\alpha P_A(x)+(1-\alpha )x$ where $\alpha \in [0,1]$ and $P_A$ is the projection onto a non-empty, convex and closed subset $A$…