This paper surveys some of the main convergence properties of the Mann-type iteration for
the demicontractive mappings. Some variants of the Mann iteration that ensure the strong …

Demicontractive operators form an important class of nonexpansive type mappings whose
study led researchers to the creation of some beautiful results in the framework of metric …

We give a brief account on a basic result (Lemma\ref {lem2}) which is a very useful tool in
proving various convergence theorems in the framework of the iterative approximation of …

In Chap. 5 we present iterative methods for solving several convex optimization problems in
a Hilbert space: the common fixed point problem, convex feasibility problem, split feasibility …

Let C be a nonempty closed convex subset of a real Hilbert space H. Let S: C→ C be a non-
expansive mapping and [Formula: see text] be an infinite family of non-expansive mappings …

We consider a projection method for convex feasibility problem that is known to converge
only weakly. Exploiting a property concerning the intersection of a family of convex closed …

Algorithms for finding the minimum norm solution of hierarchical fixed point problems Page 1
Algorithms for finding the minimum norm solution of hierarchical fixed point problems HE …

In Chap. 2 we introduce several classes of operators: nonexpansive, quasi-nonexpansive,
strictly quasi-nonexpansive, strongly quasi-nonexpansive, cutters, firmly nonexpansive …

In Chap. 4 we give examples of algorithmic projection operators and show their properties.
These properties are, in most cases, corollaries of general properties of operators presented …

Many convex optimization problems can be reduced to finding a fixed point of a
nonexpansive (or a more general operator) U: H → H. Iterative methods for solving these …