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Contracting Mapping on Normed Linear Space Cover

Contracting Mapping on Normed Linear Space

Open Access
|Feb 2013

References

  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  2. [2] Józef Białas. Properties of the intervals of real numbers. Formalized Mathematics, 3(2):263-269, 1992.
  3. [3] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  4. [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  5. [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  6. [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  7. [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  8. [8] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  9. [9] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. FormalizedMathematics, 13(4):577-580, 2005.
  10. [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/v10037-007-0008-5.10.2478/v10037-007-0008-5
  11. [11] Noboru Endou, Yasumasa Suzuki, and Yasunari Shidama. Real linear space of real sequences. Formalized Mathematics, 11(3):249-253, 2003.
  12. [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. [13] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.
  14. [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.10.2478/v10037-009-0005-y
  15. [15] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  16. [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/v10037-011-0003-8.10.2478/v10037-011-0003-8
  17. [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/v10037-012-0011-3.10.2478/v10037-012-0011-3
  18. [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.10.2478/v10037-009-0021-y
  19. [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/v10037-011-0032-3.10.2478/v10037-011-0032-3
  20. [20] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.
  21. [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. [22] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
  23. [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/v10037-011-0012-7.10.2478/v10037-011-0012-7
  24. [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/v10037-011-0008-3.10.2478/v10037-011-0008-3
  25. [25] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  26. [26] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. FormalizedMathematics, 1(4):797-801, 1990.
  27. [27] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  28. [28] Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
  29. [29] Laurent Schwartz. Cours d’analyse II, Ch. 5. HERMANN, Paris, 1967.
  30. [30] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  31. [31] Yasumasa Suzuki. Banach space of bounded real sequences. Formalized Mathematics, 12(2):77-83, 2004.
  32. [32] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  33. [33] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  34. [34] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  35. [35] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. FormalizedMathematics, 1(2):297-301, 1990.
  36. [36] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  37. [37] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  38. [38] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  39. [39] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
DOI: https://doi.org/10.2478/v10037-012-0035-8 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 291 - 301
Published on: Feb 2, 2013
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2013 Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.