N. Matar

Every Strongly Remotal Subset In Banach Spaces is a Singleton

R. Khalil & N. Matar · Journal of Advances in Mathematics and Computer Science · 2014

Let X be a Banach space, and E ⊂ X be a non-empty closed bounded subset of X. The set E is called proximinal in X if for all x ∈ X there is some e ∈ E such that ǁx - eǁ = inf{ǁx - yǁ : y ∈ E}. E is called remotal in X if for all x ∈ X, there exists e ∈ E such that ǁx - eǁ =...