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Infinite approximate Peano derivatives
Author(s):
Hajrudin
Fejzic
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2527-2536.
MSC (2000):
Primary 26A24;
Secondary 26A21
Posted:
October 15, 2002
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Abstract:
In this paper we introduce approximate Peano derivatives with infinite values allowed, and we show that these derivatives are Baire one, and possess the Darboux and Denjoy-Clarkson properties. Also we show that if they are bounded from above or below on an interval, then the corresponding ordinary derivatives exist and equal the approximate Peano derivatives.
References:
- 1.
- S. J. Agronsky, R. Biskner, A. M. Bruckner and J. Marík, Representations of Functions by Derivatives, Trans. Amer. Math. Soc. 263 (2) (1981), 493-500. MR 82e:26006
- 2.
- J. Clarkson, A Property of Derivatives, Bull. Amer. Math. Soc. 53 (1947), 124-125. MR 8:451e
- 3.
- H. Fejzic, The Peano Derivatives, Ph.D. Dissertation, Michigan State University (1992).
- 4.
- H. Fejzic, On Approximate Peano Derivatives, Acta Math. Hungar. 65 (4) (1994), 319-332. MR 95f:26006
- 5.
- H. Fejzic, J. Marík and C. Weil, Extending Peano Derivatives, Mathematica Bohemica, 119 (1994), 387-406. MR 96c:26003
- 6.
- H. Fejzic and D. Rinne, Peano Path Derivatives, Proc. Amer. Math. Soc. 125 (9) (1997), 2651-2656. MR 97j:26004
- 7.
- M. Laczkovich, D. Preiss and C. Weil, On Unilateral and Bilateral nth Peano Derivatives, Proc. Amer. Math. Soc. 99 (1987), 129-134. MR 88d:26009
- 8.
- C-M. Lee, On the Approximate Peano Derivatives, J. London Math. Soc. (2) 12 (1976), 475-478. MR 53:3222
- 9.
- J. Lipinski, Sur la discontinuité approximative et la dérivée approximative, Colloq. Math. 10 (1963), 103-109. MR 27:246
- 10.
- L. Misik, Bemerkungen über Approximative Ableitung, Mat. Cas. 19 (1969), 283-292. MR 46:1977
- 11.
- D. Preiss, Approximate Derivatives and Baire Classes, Czech. Math. J. 21 (1971), 373-382. MR 44:4158
- 12.
- S. Verblunsky, On the Peano Derivatives, Proc. London Math. Soc. 33 (1971), 313-324. MR 44:2896
- 13.
- A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Cambridge (1991).
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Additional Information:
Hajrudin
Fejzic
Affiliation:
Department of Mathematics, California State University, San Bernardino, California 92407
Email:
hfejzic@csusb.edu
DOI:
10.1090/S0002-9939-02-06828-4
PII:
S 0002-9939(02)06828-4
Received by editor(s):
January 5, 2001
Received by editor(s) in revised form:
March 27, 2002
Posted:
October 15, 2002
Communicated by:
David Preiss
Copyright of article:
Copyright
2002,
American Mathematical Society
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