Let ψ(x) be a continuous and strictly increasing function defined on [0,∞) with ψ(0)=0 and ψ(x)/x is nonincreasing. A function φ(x) is said to satisfy the condition Lip-ψ (denoted byφ ∈Lip-ψ) if there exists ...Let ψ(x) be a continuous and strictly increasing function defined on [0,∞) with ψ(0)=0 and ψ(x)/x is nonincreasing. A function φ(x) is said to satisfy the condition Lip-ψ (denoted byφ ∈Lip-ψ) if there exists a positive constant M>0 such that |φ(x)-φ(y)|(?)Mψ(|x-y|) for all x,y∈R^1. For ψ(x)=x^r,0<r(?)1, the condition Lip-x^r reduces to the usual rth order Lipschitz condition, a fact that will be denoted by Lip-r instead of Lip-x^r. Let J be the set of all those one-dimension-展开更多
文摘Let ψ(x) be a continuous and strictly increasing function defined on [0,∞) with ψ(0)=0 and ψ(x)/x is nonincreasing. A function φ(x) is said to satisfy the condition Lip-ψ (denoted byφ ∈Lip-ψ) if there exists a positive constant M>0 such that |φ(x)-φ(y)|(?)Mψ(|x-y|) for all x,y∈R^1. For ψ(x)=x^r,0<r(?)1, the condition Lip-x^r reduces to the usual rth order Lipschitz condition, a fact that will be denoted by Lip-r instead of Lip-x^r. Let J be the set of all those one-dimension-
