Previous |  Up |  Next

Article

Keywords:
Kurzweil-Henstock integral; Perron integral; KH-integral; fundamental theorem; differentiation of series
Summary:
Applications of ideal from Kurzweil-Henstock integration to elementary analysis on $\bold R$, mean value theorems for vector valued functions, l'Hospital rule, theorems of Taylor type and path independence of line integrals are discussed.
References:
[B] P. S. Bullen: Some applications of paгtitioning. Real Analysis Exch. 9 (1983-1984), 539-557. DOI 10.2307/44153567 | MR 0766078
[Bs] R. P. Boas: L'Hôpital rule without mean-value theorems. American Math. Monthly 76 (1969), 1051-1053. DOI 10.1080/00029890.1969.12000410 | MR 1535647
[Bo] M. V. Botsko: The use of full covers in Real Analysis. AMM 96 (1989), 328-333. MR 0992079 | Zbl 0721.26003
[Bol] Michael W. Botsko: A Unifìed Treatment of Vaгious Theorems in Elementery Analysis. The American Mathematical Monthly 94 (1987), 450-453. DOI 10.1080/00029890.1987.12000664 | MR 1541097
[C] John B. Conway: Functions of one comlex variable. Springeг, New York, Heidelbeгg, Berlin, 1975. MR 0447532
[He] R. Henstock: Definitions of Riemann type of the variational integrals. Proc. London Math. Soc. (3), 11 (1961), 401-418. MR 0132147 | Zbl 0099.27402
[He1] R. Henstock: Theory of Integration. Butterworths, London, 1963. MR 0158047 | Zbl 0154.05001
[He2] R. Henstock: Lineaг Analysis. Butterwoгths, London, 1967.
[HeЗ] R. Henstock: Lectures on the Theory of Integration. Woгld Scientific, Singapore, 1988. MR 0963249 | Zbl 0668.28001
[He4] R.Henstock: A Riemann Integral of Lebesgue Power. Canad. J. Math. 20(1968), 79-87. DOI 10.4153/CJM-1968-010-5 | MR 0219675
[Hu] Huntigton E. U.: Simplified proof of L'Hôpital's theorem on ideterminate forms. Bulletin of Amer. Math. Soc. 29 (1923), 207.
[K] J. Kurzweil: Generalized Ordinary Differential Equations. Czechoslovak Math. Jour. 7 (82) (1957), 418-446. MR 0111875 | Zbl 0090.30002
[K1] J. Kurzweil: Nichtabsolut Konvergente Integrale. Teubner, Leipzig, 1980. MR 0597703 | Zbl 0441.28001
[La] E.G. Landau: Differential and Integral Calculus. Chelsea, New York, 1960. MR 1849168
[Ma] J. Mawhin: Introduction à l'Analyse. Зrd ed., Cabay, Louvain-la-Neuve, 1983.
[Mc1] Robert M. McLeod: Mean Value Theorems foг Vector Valued Functions. Proc. of Edin. Math. Soc. 14 (1964-5), 197-209. MR 0185052
[Po] E. I. Poffald: The Remainder in Taylor's Formula. American Math. Monthly. 97 (1990), 205-213. DOI 10.1080/00029890.1990.11995575 | MR 1048431 | Zbl 0745.41035
[R] S. Rolewicz: Uwagi o funkcjach o pochodnej zero. Wiadomosci Matematyczne 3 (1959), 127-128. MR 0117583
[S] G. Szabó: A note on L'Hôpital's rule. Elemente der Mathematik 44 (1989), 150-153. MR 1019944 | Zbl 0702.26004
[T] H. B. Thompson: Taylor's Theorem with the integral remainder under very weak differentiable assumptions. The Gazette of the Australian Math. Soc. 12 (1985), 1-6. MR 0791272
[T1] H. B. Thompson: Taylor's Theorem using the Generalized Riemann integral. American Mathematical Monthly 96 (1989), 346-350. DOI 10.1080/00029890.1989.11972194 | MR 0992083 | Zbl 0682.26001
[Ya] Sadayuki Yamamuro: Differential Calculus in Topological Linear Spaces. Springer-Lecture Notes in Mathematics, Berlin, Heidelberg, New York, 1974, pp. 14. MR 0488118
[V1] R. Výborný: Remarks on elementary analysis. Normat 29 (1981), 72-74.
[V2] R. Výborný: On the use of a diffeгentiable homotopy in the proof of the Cauchy theorem. American Math. Monthly 86 (1979), 380-382. DOI 10.1080/00029890.1979.11994813 | MR 0528795
[VN] R. Výborný R. Nester: L'Hôpital rule, a counterexample. Elemente der Mathematik 44 (1989), 116-121. MR 1006321
Partner of
EuDML logo