Path differentiation: further unification

• Autorzy: Udayan B. Darji , Michael J. Evans
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994-1995
• Tom: 146
• Numer: 3
• Strony: 267-282

Daty

wydano

1995

otrzymano

1993-12-07

poprawiono

1994-09-26

Twórcy

autor

Udayan B. Darji

• Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.

autor

Michael J. Evans

• Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450, U.S.A.

Bibliografia

• [1] 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.
• [2] 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.
• [3] U. B. Darji, M. J. Evans and R. J. O'Malley, Condition ℬ and Baire 1 generalized derivatives, Proc. Amer. Math. Soc., to appear.
• [4] R. J. O'Malley, Selective derivates, Acta Math. Acad. Sci. Hungar. 29 (1977), 77-97.
• [5] R. J. O'Malley, The multiple intersection property for path derivatives, Fund. Math. 128 (1987), 1-6.
• [6] R. J. O'Malley, First return path derivatives, Proc. Amer. Math. Soc. 116 (1992), 73-77.
• [7] R. J. O'Malley and C. E. Weil, Selective, bi-selective, and composite differentiation, Acta Math. Acad. Sci. Hungar. 43 (1984), 31-36.