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2012 | 20 | 4 | 291-301

Tytuł artykułu

Contracting Mapping on Normed Linear Space

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

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].

Słowa kluczowe

Wydawca

Rocznik

Tom

20

Numer

4

Strony

291-301

Opis fizyczny

Daty

wydano
2012-12-01
online
2013-02-02

Twórcy

  • Ibaraki University Faculty of Engineering, Hitachi, Japan
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok Poland
  • Shinshu University, Nagano, Japan

Bibliografia

  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [2] Józef Białas. Properties of the intervals of real numbers. Formalized Mathematics, 3(2):263-269, 1992.
  • [3] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [8] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • [9] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. FormalizedMathematics, 13(4):577-580, 2005.
  • [10] 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]
  • [11] Noboru Endou, Yasumasa Suzuki, and Yasunari Shidama. Real linear space of real sequences. Formalized Mathematics, 11(3):249-253, 2003.
  • [12] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. FormalizedMathematics, 9(2):281-284, 2001.
  • [13] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.
  • [14] Artur Korniłowicz. Arithmetic operations on functions from sets into functional sets. Formalized Mathematics, 17(1):43-60, 2009, doi:10.2478/v10037-009-0005-y.[Crossref]
  • [15] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  • [16] Keiichi Miyajima, Takahiro Kato, and Yasunari Shidama. Riemann integral of functions from R into real normed space. Formalized Mathematics, 19(1):17-22, 2011, doi: 10.2478/v10037-011-0003-8.[Crossref]
  • [17] Keiichi Miyajima, Artur Korniłowicz, and Yasunari Shidama. Riemann integral of functions from R into n-dimensional real normed space. Formalized Mathematics, 20(1):79-86, 2012, doi: 10.2478/v10037-012-0011-3.[Crossref]
  • [18] Keiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.[Crossref]
  • [19] Keiko Narita, Artur Kornilowicz, and Yasunari Shidama. More on the continuity of real functions. Formalized Mathematics, 19(4):233-239, 2011, doi: 10.2478/v10037-011-0032-3.[Crossref]
  • [20] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.
  • [21] Takaya Nishiyama, Artur Korniłowicz, and Yasunari Shidama. The uniform continuity of functions on normed linear spaces. Formalized Mathematics, 12(3):277-279, 2004.
  • [22] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
  • [23] Hiroyuki Okazaki, Noboru Endou, Keiko Narita, and Yasunari Shidama. Differentiable functions into real normed spaces. Formalized Mathematics, 19(2):69-72, 2011, doi: 10.2478/v10037-011-0012-7.[Crossref]
  • [24] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces. Formalized Mathematics, 19(1):45-49, 2011, doi: 10.2478/v10037-011-0008-3.[Crossref]
  • [25] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [26] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. FormalizedMathematics, 1(4):797-801, 1990.
  • [27] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • [28] Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
  • [29] Laurent Schwartz. Cours d’analyse II, Ch. 5. HERMANN, Paris, 1967.[WoS]
  • [30] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  • [31] Yasumasa Suzuki. Banach space of bounded real sequences. Formalized Mathematics, 12(2):77-83, 2004.
  • [32] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [33] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  • [34] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [35] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. FormalizedMathematics, 1(2):297-301, 1990.
  • [36] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [37] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [38] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [39] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_v10037-012-0035-8
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