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1
Content available remote

The Sum and Product of Finite Sequences of Complex Numbers

100%
Miyajima K., Kato T.
Formalized Mathematics
|
2010
|
tom 18
|
nr 2
107-111
EN
This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].
2
Content available remote

Riemann Integral of Functions from R into R n

100%
Miyajima K., Shidama Y.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
179-185
EN
In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].
3
Content available remote

The Product Space of Real Normed Spaces and its Properties

81%
Endou N., Shidama Y., Miyajima K.
Formalized Mathematics
|
2007
|
tom 15
|
nr 3
81-85
EN
In this article, we define the product space of real linear spaces and real normed spaces. We also describe properties of these spaces.
4
Content available remote

Riemann Integral of Functions R into C

81%
Miyajima K., Kato T., Shidama Y.
Formalized Mathematics
|
2010
|
tom 18
|
nr 4
201-206
EN
In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].
5
Content available remote

Riemann Integral of Functions from R inton-dimensional Real Normed Space

81%
Miyajima K., Korniłowicz A., Shidama Y.
Formalized Mathematics
|
2012
|
tom 20
|
nr 1
79-86
EN
In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].
6
Content available remote

Partial Differentiation on Normed Linear Spaces R n

81%
Endou N., Shidama Y., Miyajima K.
Formalized Mathematics
|
2007
|
tom 15
|
nr 2
65-72
EN
Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].
7
Content available remote

Riemann Integral of Functions from R into Real Normed Space

81%
Miyajima K., Kato T., Shidama Y.
Formalized Mathematics
|
2011
|
tom 19
|
nr 1
17-22
EN
In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].
8
Content available remote

Contracting Mapping on Normed Linear Space

81%
Miyajima K., Korniłowicz A., Shidama Y.
Formalized Mathematics
|
2012
|
tom 20
|
nr 4
291-301
EN
In this article, we described the contracting mapping on normed linear space. Furthermore, we applied that mapping to ordinary differential equations on real normed space. Our method is based on the one presented by Schwarz [29].
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