ArticleOriginal scientific text
Title
Path differentiation: further unification
Authors 1, 2
Affiliations
- Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.
- Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450, U.S.A.
Abstract
A. M. Bruckner, R. J. O'Malley, and B. S. Thomson introduced path differentiation as a vehicle for unifying the theory of numerous types of generalized differentiation of real valued functions of a real variable. Part of their classification scheme was based on intersection properties of the underlying path systems. Here, additional light is shed on the relationships between these various types of path differentiation and it is shown how composite differentiation and first return differentiation fit in to this scheme.
Bibliography
- A. M. Bruckner, R. J. O'Malley and B. S. Thomson, Path derivatives: a unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), 97-125.
- U. B. Darji, M. J. Evans and R. J. O'Malley, First return path systems: differentiability, continuity, and orderings, Acta Math. Hungar. 66 (1995), 83-103.
- U. B. Darji, M. J. Evans and R. J. O'Malley, Condition ℬ and Baire 1 generalized derivatives, Proc. Amer. Math. Soc., to appear.
- R. J. O'Malley, Selective derivates, Acta Math. Acad. Sci. Hungar. 29 (1977), 77-97.
- R. J. O'Malley, The multiple intersection property for path derivatives, Fund. Math. 128 (1987), 1-6.
- R. J. O'Malley, First return path derivatives, Proc. Amer. Math. Soc. 116 (1992), 73-77.
- R. J. O'Malley and C. E. Weil, Selective, bi-selective, and composite differentiation, Acta Math. Acad. Sci. Hungar. 43 (1984), 31-36.
Additional information
http://matwbn.icm.edu.pl/ksiazki/fm/fm146/fm14635.pdf
Pages:
267-282
Main language of publication
English
Received
1993-12-07
Accepted
1994-09-26
Published
1995
Exact and natural sciences