Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces
Takao Inoué; Adam Naumowicz; Noboru Endou; Yasunari Shidama
Formalized Mathematics (2011)
- Volume: 19, Issue: 2, page 65-68
- ISSN: 1426-2630
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topTakao Inoué, et al. " Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces ." Formalized Mathematics 19.2 (2011): 65-68. <http://eudml.org/doc/266577>.
@article{TakaoInoué2011,
abstract = {In this article, we aim to prove the characterization of differentiation by means of partial differentiation for vector-valued functions on n-dimensional real normed linear spaces (refer to [15] and [16]).},
author = {Takao Inoué, Adam Naumowicz, Noboru Endou, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {65-68},
title = { Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces },
url = {http://eudml.org/doc/266577},
volume = {19},
year = {2011},
}
TY - JOUR
AU - Takao Inoué
AU - Adam Naumowicz
AU - Noboru Endou
AU - Yasunari Shidama
TI - Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces
JO - Formalized Mathematics
PY - 2011
VL - 19
IS - 2
SP - 65
EP - 68
AB - In this article, we aim to prove the characterization of differentiation by means of partial differentiation for vector-valued functions on n-dimensional real normed linear spaces (refer to [15] and [16]).
LA - eng
UR - http://eudml.org/doc/266577
ER -
References
top- [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [2] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
- [3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
- [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
- [8] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.
- [9] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.[Crossref]
- [10] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
- [11] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
- [12] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
- [13] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
- [14] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
- [15] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976.
- [16] Laurent Schwartz. Cours d'analyse. Hermann, 1981.[WoS]
- [17] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
- [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
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