| Title:
|
Some applications of Kurzweil-Henstock integration (English) |
| Author:
|
Výborný, Rudolf |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
425-441 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
Perron integral |
| Keyword:
|
KH-integral |
| Keyword:
|
fundamental theorem |
| Keyword:
|
differentiation of series |
| MSC:
|
26A24 |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| idZBL:
|
Zbl 0797.26005 |
| idMR:
|
MR1251885 |
| DOI:
|
10.21136/MB.1993.126154 |
| . |
| Date available:
|
2009-09-24T21:01:48Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126154 |
| . |
| Reference:
|
[B] P. S. Bullen: Some applications of paгtitioning.Real Analysis Exch. 9 (1983-1984), 539-557. MR 0766078, 10.2307/44153567 |
| Reference:
|
[Bs] R. P. Boas: L'Hôpital rule without mean-value theorems.American Math. Monthly 76 (1969), 1051-1053. MR 1535647, 10.1080/00029890.1969.12000410 |
| Reference:
|
[Bo] M. V. Botsko: The use of full covers in Real Analysis.AMM 96 (1989), 328-333. Zbl 0721.26003, MR 0992079 |
| Reference:
|
[Bol] Michael W. Botsko: A Unifìed Treatment of Vaгious Theorems in Elementery Analysis.The American Mathematical Monthly 94 (1987), 450-453. MR 1541097, 10.1080/00029890.1987.12000664 |
| Reference:
|
[C] John B. Conway: Functions of one comlex variable.Springeг, New York, Heidelbeгg, Berlin, 1975. MR 0447532 |
| Reference:
|
[He] R. Henstock: Definitions of Riemann type of the variational integrals.Proc. London Math. Soc. (3), 11 (1961), 401-418. Zbl 0099.27402, MR 0132147 |
| Reference:
|
[He1] R. Henstock: Theory of Integration.Butterworths, London, 1963. Zbl 0154.05001, MR 0158047 |
| Reference:
|
[He2] R. Henstock: Lineaг Analysis.Butterwoгths, London, 1967. |
| Reference:
|
[HeЗ] R. Henstock: Lectures on the Theory of Integration.Woгld Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
|
[He4] R.Henstock: A Riemann Integral of Lebesgue Power.Canad. J. Math. 20(1968), 79-87. MR 0219675, 10.4153/CJM-1968-010-5 |
| Reference:
|
[Hu] Huntigton E. U.: Simplified proof of L'Hôpital's theorem on ideterminate forms.Bulletin of Amer. Math. Soc. 29 (1923), 207. |
| Reference:
|
[K] J. Kurzweil: Generalized Ordinary Differential Equations.Czechoslovak Math. Jour. 7 (82) (1957), 418-446. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[K1] J. Kurzweil: Nichtabsolut Konvergente Integrale.Teubner, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[La] E.G. Landau: Differential and Integral Calculus.Chelsea, New York, 1960. MR 1849168 |
| Reference:
|
[Ma] J. Mawhin: Introduction à l'Analyse.Зrd ed., Cabay, Louvain-la-Neuve, 1983. |
| Reference:
|
[Mc1] Robert M. McLeod: Mean Value Theorems foг Vector Valued Functions.Proc. of Edin. Math. Soc. 14 (1964-5), 197-209. MR 0185052 |
| Reference:
|
[Po] E. I. Poffald: The Remainder in Taylor's Formula.American Math. Monthly. 97 (1990), 205-213. Zbl 0745.41035, MR 1048431, 10.1080/00029890.1990.11995575 |
| Reference:
|
[R] S. Rolewicz: Uwagi o funkcjach o pochodnej zero.Wiadomosci Matematyczne 3 (1959), 127-128. MR 0117583 |
| Reference:
|
[S] G. Szabó: A note on L'Hôpital's rule.Elemente der Mathematik 44 (1989), 150-153. Zbl 0702.26004, MR 1019944 |
| Reference:
|
[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 |
| Reference:
|
[T1] H. B. Thompson: Taylor's Theorem using the Generalized Riemann integral.American Mathematical Monthly 96 (1989), 346-350. Zbl 0682.26001, MR 0992083, 10.1080/00029890.1989.11972194 |
| Reference:
|
[Ya] Sadayuki Yamamuro: Differential Calculus in Topological Linear Spaces.Springer-Lecture Notes in Mathematics, Berlin, Heidelberg, New York, 1974, pp. 14. MR 0488118 |
| Reference:
|
[V1] R. Výborný: Remarks on elementary analysis.Normat 29 (1981), 72-74. |
| Reference:
|
[V2] R. Výborný: On the use of a diffeгentiable homotopy in the proof of the Cauchy theorem.American Math. Monthly 86 (1979), 380-382. MR 0528795, 10.1080/00029890.1979.11994813 |
| Reference:
|
[VN] R. Výborný R. Nester: L'Hôpital rule, a counterexample.Elemente der Mathematik 44 (1989), 116-121. MR 1006321 |
| . |
