Über die Stetigkeit einer Funktion von zwei Veränderlichen unter Monotonie-Bedingungen
Abstract
Let T, E, F be topological spaces, and let E, F also be preordered with some compatibility between topology and order stucture. Theorem: If f(t,x): T×E→F is separately continuous with respect to its variables and monotone non-decreasing with respect to x, then f is continuous. The case of ordered normed spaces E, F is discussed in detail.
References
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2. M.A. Krasnosel'skiĭ, G.M. Vaĭnikko, P.P. Zabreĭko, Ja.B. Rutickiĭ, V.Ja. Stecenko, Näherungsverfahren zur Lösung von Operatorgleichungen, Akademie-Verlag, Berlin 1973 [Übersetzung aus dem Russichen].
3. N.S. Kurpel', B.A. Šuvar, Dvustoronnie operatornye neravenstva i ih primenenija, Naukova Dumka, Kiev, 1980.
4. V.l. Opoĭcev, Obobščenie teorii monotonnyh i vognutyh operatorov, Trudy Moskov. Mat. Obšč. 36 (1978), 237-273.
5. J. Pfanzagl, Theory of measurement, Physica-Verlag, Würzburg - Wien, 1971.
6. R. Redheffer. Gewöhnliche Differentialungleichungen mit quasimonotonen Funktionen in normierten linearen Räumen, Arch. Rational Mech. Anal. 52 (1973), 121-133.
7. P. Volkmann, Zametka ob integral'nyh neravenstvah tipa Vol'terra, Ukrain. Mat. Ž. 36 (1984), 393-395.
8. W. Walter, Differential and integral inequalities, Springer-Verlag, Berlin - Heidelberg - New York, 1970 [Übersetzung aus dem Deutschen].
KrtschaM., & VolkmannP. (1991). Über die Stetigkeit einer Funktion von zwei Veränderlichen unter Monotonie-Bedingungen. Annales Mathematicae Silesianae, 5, 18-27. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14277
Manfred Krtscha
Fakultät für Mathematik, Universität Karlsruhe, Deutschland Germany
Fakultät für Mathematik, Universität Karlsruhe, Deutschland Germany
Peter Volkmann
Fakultät für Mathematik, Universität Karlsruhe, Deutschland Germany
Fakultät für Mathematik, Universität Karlsruhe, Deutschland Germany
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