On Simultaneous Farthest Points in 𝐿∞(𝐼,𝑋)
Let 𝑋 be a Banach space and let 𝐺 be a closed bounded subset of 𝑋. For (𝑥1,𝑥2,…,𝑥𝑚)∈𝑋𝑚, we set 𝜌(𝑥1,𝑥2,…,𝑥𝑚,𝐺)=sup{max1≤𝑖≤𝑚‖𝑥𝑖−𝑦‖∶𝑦∈𝐺}. The set 𝐺 is called simultaneously remotal if, for any (𝑥1,𝑥2,…,𝑥𝑚)∈𝑋𝑚, there exists 𝑔∈𝐺 such that 𝜌(𝑥1,𝑥2,…,𝑥𝑚,𝐺)=max1≤𝑖≤𝑚‖𝑥𝑖−𝑔‖. In this paper, we show that if...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/890598 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|