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On the extension of Lipschitz, Lipschitz-Hölder continuous, and monotone functions. (English) Zbl 0191.34603


MSC:

26A48 Monotonic functions, generalizations

Citations:

Zbl 0032.21401
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References:

[1] Stefan Banach, Wstȩp do teorii funkcji rzeczywistych, Monografie Matematyczne. Tom XVII.], Polskie Towarzystwo Matematyczne, Warszawa-Wrocław, 1951 (Polish).
[2] C. Berge and A. Ghouila-Houri, Programmes, jeux et réseaux de transport, Dunod, Paris, 1962 (French). · Zbl 0111.17302
[3] Felix E. Browder, Existence and perturbation theorems for nonlinear maximal monotone operators in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 322 – 327. · Zbl 0176.45205
[4] J. Czipszer and L. Gehér, Extension of functions satisfying a Lipschitz condition, Acta Math. Acad. Sci. Hungar. 6 (1955), 213 – 220 (English, with Russian summary). · Zbl 0064.05406
[5] Ludwig Danzer, Branko Grünbaum, and Victor Klee, Helly’s theorem and its relatives, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 101 – 180. · Zbl 0132.17401
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[9] Branko Grünbaum, A generalization of theorems of Kirszbraun and Minty, Proc. Amer. Math. Soc. 13 (1962), 812 – 814. · Zbl 0129.09202
[10] M. D. Kirszbraun, Über die zusammenziehenden and Lipschitzschen Transformationen, Fund. Math. 22 (1934), 7-10. · Zbl 0009.03904
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[12] George J. Minty, On the simultaneous solution of a certain system of linear inequalities, Proc. Amer. Math. Soc. 13 (1962), 11 – 12. · Zbl 0105.30901
[13] George J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341 – 346. · Zbl 0111.31202
[14] George J. Minty, On the generalization of a direct method of the calculus of variations, Bull. Amer. Math. Soc. 73 (1967), 315 – 321. · Zbl 0157.19103
[15] I. J. Schoenberg, On a theorem of Kirzbraun and Valentine, Amer. Math. Monthly 60 (1953), 620 – 622. · Zbl 0053.12201
[16] Sten Olof Schönbeck, Extension of nonlinear contractions, Bull. Amer. Math. Soc. 72 (1966), 99 – 101. · Zbl 0135.17603
[17] F. A. Valentine, A Lipschitz condition preserving extension for a vector function, Amer. J. Math. 67 (1945), 83 – 93. · Zbl 0061.37507
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