On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions

Luděk Zajíček

Commentationes Mathematicae Universitatis Carolinae (1981)

  • Volume: 022, Issue: 3, page 549-560
  • ISSN: 0010-2628

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Zajíček, Luděk. "On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions." Commentationes Mathematicae Universitatis Carolinae 022.3 (1981): 549-560. <http://eudml.org/doc/17128>.

@article{Zajíček1981,
author = {Zajíček, Luděk},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {approximate Dini derivates; one-sided approximate derivatives; sigma- porous sets; Baire class one functions; Jarnik-Blumberg method; Denjoy- Young-Saks theorem},
language = {eng},
number = {3},
pages = {549-560},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions},
url = {http://eudml.org/doc/17128},
volume = {022},
year = {1981},
}

TY - JOUR
AU - Zajíček, Luděk
TI - On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1981
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 022
IS - 3
SP - 549
EP - 560
LA - eng
KW - approximate Dini derivates; one-sided approximate derivatives; sigma- porous sets; Baire class one functions; Jarnik-Blumberg method; Denjoy- Young-Saks theorem
UR - http://eudml.org/doc/17128
ER -

References

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  2. A. M. BRUCKNER, Differentiation of real functions, Lecture notes in Mathematics, No. 659, Springer Verlag, 1978. (1978) Zbl0382.26002MR0507448
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  4. M. J. EVANS P. D. HUMKE, Directional cluster sets and essential directional cluster sets of гeal functions defined in the upper half plane, Rev. Roumaine Math. Pures Appl. 23 (1978), 533-542. (1978) MR0492273
  5. K. M. GARG, On asymmetrical derivates of non-differentiable functions, Can. J. Math. 20 (1968), 135-143. (1968) Zbl0194.08601MR0220878
  6. R. L. JEFFERY, The derivatives of arbitrary functions over arbitrary sets, Ann. of Mat. 36 (1935), 438-447. (1935) MR1503233
  7. L. MIŠÍK, Notes on an approximate derivative, Mat. Časop. 22 (1972), 108-114. (1972) MR0315057
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  9. H. H. PU J. D. CHEN H. W. PU, A theorem on approximate derivates, Bull. Inst. Math. Acad. Sinica 2 (1974), 87-91. (1974) MR0342654
  10. S. SAKS, Theory of the Integral, New York, 1937. (1937) Zbl0017.30004
  11. L. E. SNYDER, Approximate Stolz angle limits, Proc. Amer. Math. Soc. 17 (1966), 416-422. (1966) Zbl0158.05102MR0188383
  12. G. TOLSTOV, Sur la dérivée approximative exacte, Mat. Sb. 4 (46) (1938), 499-504. (1938) Zbl0021.01602
  13. L. ZAJÍČEK, On cluster sets of arbitrary functions, Fund. Math. 83 (1974), 197-217. (1974) MR0338294
  14. L. ZAJÍČEK, On the intersection of the sets of the right and left internal approximate derivatives, Czech. Math. Journ. 23 (1973), 629-634. (1973) MR0323969
  15. L. ZAJÍČEK, On the symmetry of Dini derivates of arbitrary functions, Comment. Math. Univ. Carolinae 22 (1981), 195-209. (1981) MR0609947

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