1934/01/01 by Hassler Whitney · 1 citation
Computer Science · Mathematics · #Optimization and Variational Analysis #Functional Equations Stability Results #Advanced Optimization Algorithms Research #Mathematics #Differentiable function #Extension (predicate logic) #Bounded function #Monotone polygon #Continuous function (set theory) #Combinatorics #Function (biology) #Discrete mathematics #Pure mathematics #Mathematical analysis #Geometry
paper · pdf · doi:10.2307/1989708
openalex publication_date 1934/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A continuous extension the author has not seen in the literature may be given as follows; we assume for simplicity that A is bounded.Let h(r) (rO) be a continuous and monotone increasing function such that A(0)=0, and if x and y are any two points of A whose distance apart is rxv, then \f(x) -f(y) \h(rxv).For any points x of E and y of A, set B(x, y)=f(y)-h(rxi); then if x is in .4,B(x,y)f(x).The continuous extension of f(x) is,F(x), which at each point x of equals the maximum of H(x, y) as y varies over A. 63