This is a preview of subscription content, log in via an institution to check access.
References
V. V. Goncharov and A. A. Tolstonogov, “Common continuous selections of multivalued mappings with nonconvex values and their applications,” Mat. Sb.,182, No. 7, 946–969 (1991).
A. Fryszkowski, “Continuous selections for a class of nonconvex multivalued maps,” Studia Math.,76, No. 2, 163–174 (1983).
A. Bressan and G. Colombo, “Extensions and selections of maps with decomposable values,” Studia Math.,90, No. 1, 69–86 (1988).
A. Ornelas, Approximation of Relaxed Solutions for Lower Semicontinuous Differential Inclusions [Preprint, International School for Advanced Studies; No. 102/86/M], Italy, Trieste (1986).
A. I. Bulgakov, “On the question of existence of continuous branches for multivalued mappings with nonconvex images in spaces of summable functions,” Mat. Sb.,136, No. 2, 292–300 (1988).
A. A. Tolstonogov, “Extremal selectors of multivalued mappings and the ‘bang-bang’ principle for evolution inclusions,” Dokl. Akad. Nauk SSSR,317, No. 3, 589–593 (1991).
P. R. Halmos, Measure Theory [Russian translation], Izdat. Inostr. Lit., Moscow (1953).
J. L. Kelley, General Topology [Russian translation], Nauka, Moscow (1981).
R. E. Edwards, Functional Analysis. Theory and Applications [Russian translation], Mir, Moscow (1969).
K. Kuratowski, Topology. Vol. I [Russian translation], Mir, Moscow (1966).
A. A. Tolstonogov, “On certain properties of spaces of sublinear functionals,” Sibirsk. Mat. Zh.,18, No. 2, 429–443 (1977).
A. A. Tolstonogov and V. V. Goncharov, “On sublinear functionals defined on the space of Bochner integrable functions,” Sibirsk. Mat. Zh.,35, No. 1, 194–206 (1994).
E. Michael, “Continuous selections. I,” Ann. of Math. (2),63, 361–382 (1956).
F. S. De Blasi and G. Pianigiani, “Remarks on Hausdorff continuous multifunctions and selections,” Comment. Math. Univ. Carolin.,24, No. 3, 553–561 (1983).
F. Hiai and H. Umegaki, “Integrals, conditional expectations, and martingales of multivalued functions,” J. Multivariate Anal.,7, No. 1, 149–182 (1977).
Van Chu'o'ng Phan, “A density theorem with an application in relaxation of nonconvex-valued differential equations,” Sém. Anal. Convexe, Univ. Sci. Tech. Languedoc,15, No. 2, 2.1–2.22 (1985).
Author information
Authors and Affiliations
Additional information
The research was financially supported by the Russian Foundation for Fundamental Research (Grant 93-011-264).
Translated from Sibirskii Matematicheskii, Vol. 35, No. 3, pp. 537–553, May–June, 1994.
Rights and permissions
About this article
Cite this article
Goncharov, V.V., Tolstonogov, A.A. Continuous selections for a family of nonconvex-valued mappings with noncompact domain. Sib Math J 35, 479–494 (1994). https://doi.org/10.1007/BF02104812
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02104812