TY - JOUR T1 - Order-Preserving Variants of the Basic Principles of Functional Analysis AU - Zaitov, Adilbek PY - 2019 DA - June Y2 - 2019 DO - 10.33401/fujma.503688 JF - Fundamental Journal of Mathematics and Applications JO - Fundam. J. Math. Appl. PB - Fuat USTA WT - DergiPark SN - 2645-8845 SP - 10 EP - 17 VL - 2 IS - 1 LA - en AB - 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. KW - Functional analysis KW - Order-preserving functional KW - Vector space with an order unit CR - [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. CR - [2] T. Radul, Idempotent measures: Absolute retracts and soft maps, (2018), arXiv:1810.09140v1 [math.GN]. CR - [3] W. Rudin, Functional Analysis (2nd edition), International Editions (McGraw-Hill Book Co – Singapore for manufacture and export), 1991. CR - [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 CR - [5] A. Zaitov, On extension of order-preserving functionals, Doklady Akademii Nauk Uzbekistan, 5 (2005), 3-7. CR - [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. CR - [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. CR - [8] V. Paulsen, M. Tomforde, Vector spaces with an order unit, Indiana Univ. Math. J., 58(3) (2009), 1319-1359. UR - https://doi.org/10.33401/fujma.503688 L1 - https://dergipark.org.tr/en/download/article-file/737390 ER -