The aim of this note is to fill in a gap in our previous paper in this journal. Precisely, we give a new proof of the following theorem: let (0, A, +) be a \_-finite measure space with +(0)>0, 0<p<+ , and Y a separable subspace of a Banach space X. Then Y is proximinal in X iff L p (+, Y) is proximi
Constructing Best Approximations on a Jordan Curve
โ Scribed by Douglas Bridges; Wang Yuchuan
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 249 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
โฆ Synopsis
It is shown, within Bishop's constructive mathematics, that if a point is sufficiently close to a differentiable Jordan curve with suitably restricted curvature, then that point has a unique closest point on the curve.
๐ SIMILAR VOLUMES
Let C be a closed bounded convex subset of a Banach space E which has the origin of E as an interior point and let p C denote the Minkowski functional with respect to C. Given a closed set X/E and a point u # E we consider a minimization problem min C (u, X ) which consists in proving the existence
We investigate rational approximations รฐr=p; q=pร or รฐr=p; q=rร to points on the curve รฐa; a t ร for almost all a > 0; where p; q; r are all primes. We immediately obtain corollaries on making p; ยฝap; ยฝa t p simultaneously prime. # 2002 Elsevier Science (USA)