Boundary point algorithms for minimum norm fixed points of nonexpansive mappings

Finding Minimum Norm Fixed Point of Nonexpansive Mappings and Applications

Iterative algorithms for finding fixed point of nonexpansive mappings are very interesting topic due to the fact that many nonlinear problems can be reformulated as fixed point equations of nonexpansive mappings. Related works can be found in 1–32 . On the other hand, we notice that it is quite often to seek a particular solution of a given nonlinear problem, in particular, the minimum-norm sol...

Minimum-Norm Fixed Point of Pseudocontractive Mappings

and Applied Analysis 3 where K and Q are nonempty closed convex subsets of the infinite-dimension real Hilbert spaces H1 and H2, respectively, and A is bounded linear mapping from H1 to H2. Equation 1.9 models many applied problems arising from image reconstructions and learning theory see, e.g., 4 . Someworks on the finite dimensional setting with relevant projectionmethods for solving image r...

Approximating fixed points of generalized nonexpansive mappings

Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications

This paper deals with iterative methods for approximating the minimum-norm common fixed point of nonexpansive mappings. The proposed cyclic iterative algorithms and simultaneous iterative algorithms combined with a relaxation factor, which make them more flexible to solve the considered problem. Under certain conditions on the parameters, we prove that the sequences generated by the proposed it...

Fixed Point Theorems for Nonexpansive Mappings Satisfying Certain Boundary Conditions1

Let K be a bounded closed convex subset of a Banach space X with int K 40, and suppose K has the fixed point property with respect to nonexpansive self-mappings (i.e., mappings U: K^K such that \\U(x) U(y)\\ < ||* y||, x,y € K). Let T: K -X be nonexpansive and satisfy inf{||* T(x)\\: x e boundary K, T'x) /Kl > 0. It is shown that if in addition, either (i) T satisfies the Leray-Schauder boundar...