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Zbl 1065.47048
Matoušková, Eva; Reich, Simeon
The Hundal example revisited.
(English)
[J] J. Nonlinear Convex Anal. 4, No. 3, 411-427 (2003). ISSN 1345-4773; ISSN 1880-5221/e

{\it H. Hundal} [Nonlinear Anal., Theory Methods Appl. 57, No. 1, 35--61 (2004; Zbl 1070.46013)] solved an open problem by constructing an ingenious example of cone and a half-space in the Hilbert space $l_2$ which intersect at the origin, such that the corresponding sequence of alternating nearest point mappings does not convergence in norm to zero.\par In the present paper, the authors, using geometric insight, modify Hundal's example and simplify its verification. In modified example, the cone and the half-space may be disjoint. They also establish several weak and strong convergence theorems for products and convex combinations of retractions. These results provide the background for the Hundal example and its modifications.
[Jarosław Górnicki (Rzeszów)]
MSC 2000:
*47H09 Mappings defined by "shrinking" properties
41A65 Abstract approximation theory
47H30 Particular nonlinear operators
47J25 Methods for solving nonlinear operator equations (general)
47N10 Appl. of operator theory in optimization, math. programming, etc.
90C25 Convex programming

Citations: Zbl 1070.46013

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