Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The generalized Zahorski class structure of symmetric derivatives


Author: Lee Larson
Journal: Trans. Amer. Math. Soc. 282 (1984), 45-58
MSC: Primary 26A24
DOI: https://doi.org/10.1090/S0002-9947-1984-0728702-3
MathSciNet review: 728702
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A generalized Zahorski class structure is demonstrated for symmetric derivatives. A monotonicity theorem is proved and a condition sufficient to ensure that a symmetric derivative has the Darboux property is presented.


References [Enhancements On Off] (What's this?)

  • [1] C. L. Belna, M. J. Evans and P. D. Humke, Symmetric and ordinary differentiation, Proc. Amer. Math. Soc. 72 (1978), 261-267. MR 507319 (80d:26006)
  • [2] A. Bruckner, Differentiation of real functions, Lecture Notes in Math., vol. 659, Springer-Verlag, Berlin, 1978. MR 507448 (80h:26002)
  • [3] M. J. Evans, A symmetric condition for monotonicity, Bull. Inst. Math. Acad. Sinica 6 (1978), 85-91. MR 0499025 (58:17002)
  • [4] K. Garg, On a new definition of derivative, Bull. Amer. Math. Soc. 82 (1976), 768-770. MR 0409734 (53:13486)
  • [5] A. Khintchine, Recherches sur la structure des fonctions mesurables, Fund. Math. 9 (1927), 212-279.
  • [6] N. K. Kundu, On symmetric derivatives and on properties of Zahorski, Czechoslovak. Math. J. 26 (1976), 154-160. MR 0399377 (53:3221)
  • [7] L. Larson, The symmetric derivative, Trans. Amer. Math. Soc. 277 (1983), 589-599. MR 694378 (84j:26009)
  • [8] C. E. Weil, A property for certain derivatives, Indiana Univ. Math. J. 23 (1973), 527-536. MR 0335703 (49:483)
  • [9] Z. Zahorski, Sur la premiere dériveé, Trans. Amer. Math. Soc. 69 (1950), 1-54. MR 0037338 (12:247c)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26A24

Retrieve articles in all journals with MSC: 26A24


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0728702-3
Keywords: Symmetric derivative, Baire class one, Darboux property, Zahorski classes, nonangular
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society