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Order-Preserving Variants of the Basic Principles of Functional Analysis

Year 2019, Volume: 2 Issue: 1, 10 - 17, 17.06.2019
https://doi.org/10.33401/fujma.503688

Abstract

We will establish order-preserving versions of the basic principles of functional analysis such as Hahn-Banach, Banach-Steinhaus, open mapping, and Banach-Alaoglu theorems.

References

  • [1] M. Grabisch, M. Roubens, Application of the Choquet Integral in Multicriteria Decision Making, In the book ‘Fuzzy Measures and Integrals – Theory and Applications’ (eds M. Grabisch, T. Murofushi, M. Sugeno), Physica Verlag, (2000), 348-374.
  • [2] T. Radul, Idempotent measures: Absolute retracts and soft maps, (2018), arXiv:1810.09140v1 [math.GN].
  • [3] W. Rudin, Functional Analysis (2nd edition), International Editions (McGraw-Hill Book Co – Singapore for manufacture and export), 1991.
  • [4] A. Peperko, Uniform boundedness principle for nonlinear operators on cones of functions, Hindawi J. Func. Spaces, 2018, Article ID 6783748, 5 pages, available at https://doi.org/10.1155/2018/6783748
  • [5] A. Zaitov, On extension of order-preserving functionals, Doklady Akademii Nauk Uzbekistan, 5 (2005), 3-7.
  • [6] A. Zaitov, Banach-Alaoglu theorem for order-preserving functionals, Theses of reports of the international scientific conference ”Operator Algebras and Quantum Probability Theory”, Tashkent, (2005), 81-83.
  • [7] A. Zaitov, Open mapping theorem for order-preserving operators, The collection of theses of the International conference of young scientists devoted 1000 to the anniversary of Mamun Academy of Khwarezm, Tashkent, (2006), 4-5.
  • [8] V. Paulsen, M. Tomforde, Vector spaces with an order unit, Indiana Univ. Math. J., 58(3) (2009), 1319-1359.
Year 2019, Volume: 2 Issue: 1, 10 - 17, 17.06.2019
https://doi.org/10.33401/fujma.503688

Abstract

References

  • [1] M. Grabisch, M. Roubens, Application of the Choquet Integral in Multicriteria Decision Making, In the book ‘Fuzzy Measures and Integrals – Theory and Applications’ (eds M. Grabisch, T. Murofushi, M. Sugeno), Physica Verlag, (2000), 348-374.
  • [2] T. Radul, Idempotent measures: Absolute retracts and soft maps, (2018), arXiv:1810.09140v1 [math.GN].
  • [3] W. Rudin, Functional Analysis (2nd edition), International Editions (McGraw-Hill Book Co – Singapore for manufacture and export), 1991.
  • [4] A. Peperko, Uniform boundedness principle for nonlinear operators on cones of functions, Hindawi J. Func. Spaces, 2018, Article ID 6783748, 5 pages, available at https://doi.org/10.1155/2018/6783748
  • [5] A. Zaitov, On extension of order-preserving functionals, Doklady Akademii Nauk Uzbekistan, 5 (2005), 3-7.
  • [6] A. Zaitov, Banach-Alaoglu theorem for order-preserving functionals, Theses of reports of the international scientific conference ”Operator Algebras and Quantum Probability Theory”, Tashkent, (2005), 81-83.
  • [7] A. Zaitov, Open mapping theorem for order-preserving operators, The collection of theses of the International conference of young scientists devoted 1000 to the anniversary of Mamun Academy of Khwarezm, Tashkent, (2006), 4-5.
  • [8] V. Paulsen, M. Tomforde, Vector spaces with an order unit, Indiana Univ. Math. J., 58(3) (2009), 1319-1359.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Adilbek Zaitov 0000-0002-2248-0442

Publication Date June 17, 2019
Submission Date December 27, 2018
Acceptance Date February 20, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Zaitov, A. (2019). Order-Preserving Variants of the Basic Principles of Functional Analysis. Fundamental Journal of Mathematics and Applications, 2(1), 10-17. https://doi.org/10.33401/fujma.503688
AMA Zaitov A. Order-Preserving Variants of the Basic Principles of Functional Analysis. Fundam. J. Math. Appl. June 2019;2(1):10-17. doi:10.33401/fujma.503688
Chicago Zaitov, Adilbek. “Order-Preserving Variants of the Basic Principles of Functional Analysis”. Fundamental Journal of Mathematics and Applications 2, no. 1 (June 2019): 10-17. https://doi.org/10.33401/fujma.503688.
EndNote Zaitov A (June 1, 2019) Order-Preserving Variants of the Basic Principles of Functional Analysis. Fundamental Journal of Mathematics and Applications 2 1 10–17.
IEEE A. Zaitov, “Order-Preserving Variants of the Basic Principles of Functional Analysis”, Fundam. J. Math. Appl., vol. 2, no. 1, pp. 10–17, 2019, doi: 10.33401/fujma.503688.
ISNAD Zaitov, Adilbek. “Order-Preserving Variants of the Basic Principles of Functional Analysis”. Fundamental Journal of Mathematics and Applications 2/1 (June 2019), 10-17. https://doi.org/10.33401/fujma.503688.
JAMA Zaitov A. Order-Preserving Variants of the Basic Principles of Functional Analysis. Fundam. J. Math. Appl. 2019;2:10–17.
MLA Zaitov, Adilbek. “Order-Preserving Variants of the Basic Principles of Functional Analysis”. Fundamental Journal of Mathematics and Applications, vol. 2, no. 1, 2019, pp. 10-17, doi:10.33401/fujma.503688.
Vancouver Zaitov A. Order-Preserving Variants of the Basic Principles of Functional Analysis. Fundam. J. Math. Appl. 2019;2(1):10-7.

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