/pdf/problema-vypuklosti-chebyshevskikh-mnozhestv-the-problem-of-48uwyxkxyu.pdf

Проблема выпуклости чебышeвских множеств@@@The problem of convexity of Chebyshev sets

A generalization of local uniform convexity of the norm

On continuity of metric projections

The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

/pdf/some-results-on-fixed-and-best-proximity-points-of-2ar9ywuwlu.pdf

Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order

In the paper “Some remarks on approximative compactness”, Rev. Roumaine Math. Pures Appl . 9 (1964), Ivan Singer proved that if K is an approximatively compact Chebyshev set in a metric space, then the metric projection onto K is continuous. The object of this paper is to show that though, in general, the continuity of the metric projection supported by a Chebyshev set does not imply that the set is approximatively compact, it is indeed so in a large class of Banach spaces, including the locally uniformly convex spaces. It is also proved that in such a space X the metric projection onto a Chebyshev set is continuous on a set dense in X .

B.B. Panda

Papers

Approximative compactness and continuity of metric projections