A conjectured class of scale-invariant distances on inner product spaces

الأصل · EN

Let V be an inner product space, and x, y ∈ V; the conjecture is made that, for any p ∈ [1, ∞], the function dₚ(x, y):=x-y/(xᵖ+ yᵖ)¹/ᵖ is a distance on V.