Examples



mdbootstrap.com



 
Статья
2018

Metrization of a Space of Weakly Additive Functionals


K. BekzhanovaK. Bekzhanova
Русская математика
https://doi.org/10.3103/S1066369X18030015
Abstract / Full Text

We investigate a space of weakly additive, order-preserving, normed and positively homogeneous functionals on a metric compact. We construct an analog of modified Kantorovich–Rubinshtein metric on a space O(X) of weakly additive normed functionals on a metric compact X.

Author information
  • Karakalpak State University named after Berdakh, ul. Academician Abdirov 1, Nukus, 230113, Republic of UzbekistanK. Bekzhanova
References
  1. Albeverio, S., Ayupov, Sh. A., Zaitov, A. A. “On Certain Properties of the Space of Order-Preserving Functionals”, Topology Appl. 155, No. 16, 1792–1799 (2008).
  2. Davletov, D. E., Djabbarov, G. F. “Functor of Semi-Additive Functionals”, Meth. Funct. Anal. Topology 14, No. 4, 314–322 (2008).
  3. Djabbarov, G. F. “Description of Extremal Points of the Space ofWeakly Additive Positively-Homogeneous Functionals of the Two-Point Set”, Uzb.Math. J., No. 3, 17–25 (2005).
  4. Djabbarov, G. F. “Categorical Properties of the Functor of Weakly Additive Positively-Homogeneous Functionals”, Uzb. Math. J., No. 2, 20–28 (2006).
  5. Karchevska, L., Radul, T. “On Extension of Functors”, Comment. Math. Univ. Carolin. 53, No. 2, 269–279 (2012).
  6. Radul, T. “On the Functor of Order-Preserving Functionals”, Comment. Math. Univ. Carolin. 39, No. 3, 609–615 (1998).
  7. Shapiro, L. “On Operators of Extension of Functions and Normal Functors”, VestnikMosk. Univ., No. 1, 35–42 (1992).
  8. Valov, V. “Extenders and κ-Metrizable Compacts”, Math.Notes 89, No. 3–4, 319–327 (2011).
  9. Litvinov, G. L. “The Maslov Dequantization, Idempotent and Tropical mathematics: A Brief Introduction”, Zap. Nauchn. Sem. POMI 326, 145–182 (2005).
  10. Kantorovich, L. M., Rubinshtein, G. Sh. “On a Functional Space and Sertain Extremum Pproblems”, Dokl. Akad. Nauk SSSR 115, 1058–1061 (1957) [in Russian].
  11. Kantorovich, L. M., Rubinshtein, G. Sh. “On a Space of Completely Additive Functions.”, Vestn. Leningr. Univ. 13, 7, Ser.Mat.Mekh. Astron., No. 2, 52–59 (1958). [in Russian].