  We give properties of strict pseudocontractions and demicontractions defined
on a Hilbert space, which constitute wide classes of operators that arise in
iterative methods for solving fixed point problems. In particular, we give
necessary and sufficient conditions under which a convex combination and
composition of strict pseudocontractions as well as demicontractions that share
a common fixed point is again a strict pseudocontraction or a demicontraction,
respectively. Moreover, we introduce a generalized relaxation of composition of
demicontraction and give its properties. We apply these properties to prove the
weak convergence of a class of algorithms that is wider than the
Douglas-Rachford algorithm and projected Landweber algorithms. We have also
presented two numerical examples, where we compare the behavior of the
presented methods with the Douglas-Rachford method.
