Menu: Home :: go to Journal :: switch to Russian :: switch to English
You are here: all Journals and Issues→ Journal→ Issue→ Article

The set of regularity of a multivalued mapping in a space with a vector-valued metric

Annotation

We consider multivalued mappings acting in spaces with a vector-valued metric. A vector-valued metric is understood as a mapping satisfying the axioms “of an ordinary metric” with values in the cone of a linear normed space. The concept of the regularity set of a multivalued mapping is defined. A set of regularity is used in the study of inclusions in spaces with a vector-valued metric.

Keywords

multi-valued mapping; space with vector-valued metric; metric regularity; Lipschitz mapping; inclusion

Full-text in one file

Download

DOI

10.20310/1810-0198-2019-24-125-39-46

UDC

515.124.2, 515.126.4, 517.988.52

Pages

39-46

References

[1] E. S. Zhukovskii, E. A. Pluzhnikova, “Covering mappings in a product of metric spaces and boundary value problems for differential equations unsolved for the derivative”, Differential Equations, 49:4 (2013), 420–436. [2] E. S. Zhukovskii, E. A. Pluzhnikova, “On controlling objects whose motion is defined by implicit nonlinear differential equations”, Autom. Remote Control, 76:1 (2015), 24–43. [3] V. S. Treshchev, “Well-posed solvability of systems of operator equations with vector covering mappings”, Tambov University Reports. Series: Natural and Technical Sciences, 20:5 (2015), 1487–1489 (In Russian). [4] E. S. Zhukovskii, “Perturbations of vectorial coverings and systems of equations in metric spaces”, Sibirsk. Mat. Zh., 57:2 (2016), 230–241. [5] E. S. Zhukovskiy, “On coincidence points for vector mappings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, №10, 10–22. [6] E. S. Zhukovskii, “On coincidence points of multivalued vector mappings of metric spaces”, Mathematical Notes, 100:3 (2016), 363–379. [7] M. V. Borzova, T. V. Zhukovskaia, E. S. Zhukovskiy, “On covering of set-valued mappings in cartesian products of metric spaces”, Tambov University Reports. Series: Natural and Technical Sciences, 21:2 (2016), 363–370 (In Russian). [8] E. S. Zhukovskiy, “On perturbations of covering mappings in spaces with vector-valued metrics”, Tambov University Reports. Series: Natural and Technical Sciences, 21:2 (2016), 375–379 (In Russian). [9] A. V. Arutyunov, S. E. Zhukovskiy, “Coincidence points of mappings in vector metric spaces with applications to differential equations and control systems”, Differential Equations, 53:11(2017), 1440–1448. [10] E. A. Pluzhnikova, T. V. Zhukovskaia, Yu. A. Moiseev, “On sets of metric regularity of mappings in spaces with vector-valued metric”, Tambov University Reports. Series: Natural and Technical Sciences, 23:123 (2018), 547–554 (In Russian). [11] E. S. Zhukovskiy, E. A. Pluzhnikova, “Multi-valued covering maps spaces with vector-valued metrics in research of functional inclusions”, Tambov University Reports. Series: Natural and Technical Sciences, 21:6 (2016), 1974–1982 (In Russian). [12] E. S. Zhukovskiy, E. A. Panasenko, “On fixed points of multivalued mappings in spaces with a vector-valued metric”, Proceedings of Krasovskii Institute of Mathematics and Mechanics UB RAS, 24:1 (2018), 93–105 (In Russian). [13] Functional Analysis, SMB, ed. S. G. Krein, Nauka, Moscow, 1972 (In Russian).

Section of issue

Scientific articles

Для корректной работы сайта используйте один из современных браузеров. Например, Firefox 55, Chrome 60 или более новые.