in this paper, we study projected non-stationary simultaneous it-erative reconstruction techniques (p-sirt). based on algorithmic op-erators, convergence result are adjusted with opial’s theorem. the advantages of p-sirt are demonstrated on examples taken from to-mographic imaging.

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

The Douglas-Rachford algorithm can be represented as the fixed point iteration of a firmly nonexpansive operator. When operator has no points, algorithm's iterates diverge, but difference between consecutive converges to so-called minimal displacement vector, which used certify infeasibility an optimization problem. In this paper, we establish new properties allow us generalize some existing re...

We study the convergence of the Mann Iteration applied to the partial complement of a firmly nonexpansive operator with respect to a linear subspace of a Hilbert space. A new concept considered here. A regularized version is also proposed. Furthermore, to motivate this concept, some applications to robust regression procedures and location problems are proposed.

where U : H1 → H1 and T : H2 → H2 are two firmly quasi-nonexpansive operators with nonempty fixed-point sets F(U) = {x ∈ H1 : Ux = x} and F(T ) = {x ∈ H2 : Tx = x}. Note that by taking H2 = H3 and B = I, we recover the split common fixed-point problem originally introduced in Censor and Segal (J. Convex Anal. 16:587-600, 2009). In this paper, we will continue to consider the split common fixed-...

Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood and analyzed from the alternative viewpoint of firmly nonexpansive mappings, which were found to be precisely the resolvents of monotone operators. For examp...