On topological properties of sets admitting varisolvent functions
HTML articles powered by AMS MathViewer
- by D. Braess PDF
- Proc. Amer. Math. Soc. 34 (1972), 453-456 Request permission
Abstract:
Mairhuber’s theorem on Haar subspaces is generalized for the nonlinear case, where varisolvent functions are considered.References
- Dietrich Braess, On varisolvency and alternation, J. Approximation Theory 12 (1974), 230–233. MR 364976, DOI 10.1016/0021-9045(74)90064-1
- Philip C. Curtis Jr., $n$-parameter families and best approximation, Pacific J. Math. 9 (1959), 1013–1027. MR 108670
- Charles B. Dunham, Unisolvence on multidimensional spaces, Canad. Math. Bull. 11 (1968), 469–474. MR 235362, DOI 10.4153/CMB-1968-056-6
- John C. Mairhuber, On Haar’s theorem concerning Chebychev approximation problems having unique solutions, Proc. Amer. Math. Soc. 7 (1956), 609–615. MR 79672, DOI 10.1090/S0002-9939-1956-0079672-3
- John R. Rice, The approximation of functions. Vol. 2: Nonlinear and multivariate theory, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0244675
- I. J. Schoenberg and C. T. Yang, On the unicity of solutions of problems of best approximation, Ann. Mat. Pura Appl. (4) 54 (1961), 1–12. MR 141927, DOI 10.1007/BF02415339
- K. Sieklucki, Topological properties of sets admitting the Tschebycheff systems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 603–606. MR 0100192
- Ivan Singer, Cea mai bună aproximare în spaţii vectoriale normate prin elemente din subspaţii vectoriale, Editura Academiei Republicii Socialiste România, Bucharest, 1967 (Romanian). MR 0235368
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 453-456
- MSC: Primary 41A65
- DOI: https://doi.org/10.1090/S0002-9939-1972-0301431-3
- MathSciNet review: 0301431