Zur Theorie der nichtlinearen Tschebyscheff-Approximation mit Nebenbedingungen

This paper deals with questions of nonlinear Tschebyscheff-approximation theory, the approximations being constrained by nonlinear relations. We assume the approximating functions depending Fréchet-differentiable on a parameter and the constraints satisfying certain regularity and differentiability properties. Under these hypotheses in the main theorem we give necessary conditions to characterisize best approximations. Using these results, some problems in approximating functions, the best approximations being regarded to satisfy interpolatory conditions, are discussed. We deduce, that in this case best approximations admit a characterisation by generalized alternants.

---

---

Erster Teil einer gekürzten Fassung der Dissertation des Verfassers [1968].