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Let X be a Banach space, S (X) be the unit sphere of X, ψ be a function: S ( X)→ S ( X * )such that ψ(x)∈ x, and vψ(ε)=inf ,0 ≤ ε ≤ 2, where x is the set of norm 1 supporting functionals of S (X) at x. A geometric concept,modulus of V-convexity V(ε) = s