# Differentiation in Normed Spaces

Noboru Endou; Yasunari Shidama

Formalized Mathematics (2013)

- Volume: 21, Issue: 2, page 95-102
- ISSN: 1426-2630

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topNoboru Endou, and Yasunari Shidama. "Differentiation in Normed Spaces." Formalized Mathematics 21.2 (2013): 95-102. <http://eudml.org/doc/266646>.

@article{NoboruEndou2013,

abstract = {In this article we formalized the Fréchet differentiation. It is defined as a generalization of the differentiation of a real-valued function of a single real variable to more general functions whose domain and range are subsets of normed spaces [14].},

author = {Noboru Endou, Yasunari Shidama},

journal = {Formalized Mathematics},

keywords = {formalization of Fréchet derivative; Fréchet differentiability},

language = {eng},

number = {2},

pages = {95-102},

title = {Differentiation in Normed Spaces},

url = {http://eudml.org/doc/266646},

volume = {21},

year = {2013},

}

TY - JOUR

AU - Noboru Endou

AU - Yasunari Shidama

TI - Differentiation in Normed Spaces

JO - Formalized Mathematics

PY - 2013

VL - 21

IS - 2

SP - 95

EP - 102

AB - In this article we formalized the Fréchet differentiation. It is defined as a generalization of the differentiation of a real-valued function of a single real variable to more general functions whose domain and range are subsets of normed spaces [14].

LA - eng

KW - formalization of Fréchet derivative; Fréchet differentiability

UR - http://eudml.org/doc/266646

ER -

## References

top- [1] Grzegorz Bancerek. Konig’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
- [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
- [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [5] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
- [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
- [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [8] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- [11] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
- [12] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
- [13] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
- [14] Laurent Schwartz. Cours d’analyse. Hermann, 1981.[WoS]
- [15] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
- [16] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- [17] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
- [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
- [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
- [21] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.

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