# Path differentiation: further unification

Fundamenta Mathematicae (1995)

- Volume: 146, Issue: 3, page 267-282
- ISSN: 0016-2736

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topDarji, Udayan, and Evans, Michael. "Path differentiation: further unification." Fundamenta Mathematicae 146.3 (1995): 267-282. <http://eudml.org/doc/212066>.

@article{Darji1995,

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.},

author = {Darji, Udayan, Evans, Michael},

journal = {Fundamenta Mathematicae},

keywords = {path differentiation; generalized differentiation; path systems; composite differentiation; first return differentiation},

language = {eng},

number = {3},

pages = {267-282},

title = {Path differentiation: further unification},

url = {http://eudml.org/doc/212066},

volume = {146},

year = {1995},

}

TY - JOUR

AU - Darji, Udayan

AU - Evans, Michael

TI - Path differentiation: further unification

JO - Fundamenta Mathematicae

PY - 1995

VL - 146

IS - 3

SP - 267

EP - 282

AB - 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.

LA - eng

KW - path differentiation; generalized differentiation; path systems; composite differentiation; first return differentiation

UR - http://eudml.org/doc/212066

ER -

## References

top- [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. Zbl0541.26003
- [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. Zbl0821.26006
- [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. Zbl0345.26003
- [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. Zbl0762.26004
- [7] R. J. O'Malley and C. E. Weil, Selective, bi-selective, and composite differentiation, Acta Math. Acad. Sci. Hungar. 43 (1984), 31-36. Zbl0542.26006

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