In mathematics, a uniformly smooth space is a normed vector space X {\displaystyle X} satisfying the property that for every ϵ > 0 {\displaystyle \epsilon >0} there exists δ > 0 {\displaystyle \delta >0} such that if x, y ∈ X {\displaystyle x,y\in X} with ‖ x ‖ = 1 {\displaystyle \|x\|=1} and ‖ y ‖ ≤ δ {\displaystyle \|y\|\leq \delta } then ‖ x + y ‖ + ‖ x − y ‖ ≤ 2 + ϵ ‖ y ‖. Wikipedia