This is a preview of subscription content, log in via an institution to check access.
Literature Cited
V. L. Makarov and A. M. Rubinov, The Mathematical Theory of Economic Dynamics and Equilibrium [in Russian], Nauka, Moscow (1973).
A. M. Rubinov, “Sublinear operators and their applications,” Usp. Mat. Nauk,32, No. 4, 113–174 (1977).
V. L. Makarov and A. M. Rubinov, “Sublinear point-set mappings and models of economic dynamics,” Usp. Mat. Nauk25, No. 5, 125–169 (1970).
Yu. É. Linke, “On support sets of sublinear operators” Dokl. Akad. Nauk SSSR,207, No. 3, 531–533 (1972).
Yu. É. Linke, “Sublinear operators and Lindenstrauss spaces,” Dokl. Akad. Nauk SSSR,234, No. 1, 26–28 (1977).
L. Hörmander, “Sur la fonction d'appui des ensembles convexes dans une espace localement convexe,” Arkiv Mat.,3, No. 2, 181–186 (1954).
D. P. Mil'man, “Facial characteristics of convex sets; extremal elements” Tr. Mosk. Mat. Obshch.,22, 63–126 (1970).
A. M. Rubinov, “Sublinear functionals defined on a cone,” Sib. Mat. Zh.,11, No. 2, 429–441 (1970).
M. M. Fel'dman, “On sublinear operators defined on a cone,” Sib. Mat. Zh.,16, No. 6, 1308–1321 (1975).
S. S. Kutateladze and A. M. Rubinov, Minkowski Duality and Its Applications [in Russian], Nauka, Moscow (1976).
H. E. Lacey, “On the classification of Lindenstrauss spaces,” Pac. J. Math.,47 No. 1, 139–145 (1973).
E. Michael, “Continuous selections. I,” Ann. of Math.,63, No. 2, 361–382 (1956).
L. Asimov, “Affine selections on simplicially split compact convex sets,” J. London Math. Soc.,6, No. 3, 533–538 (1979).
T. Wada, “Weakly compact linear operators on function spaces,” Osaka Mat. J.,13, No. 1, 169–181 (1961).
R. G. Bartle, “On compactness in functional analysis,” Trans. Am. Math. Soc.,79, No. 1, 35–37 (1955).
R. E. Edwards, Functional Analysis, Theory and Applications, Holt, Rinehart, and Winston, New York (1965).
H. H. Schafer, Topological Vector Spaces, Macmillan, New York (1966).
N. Bourbaki, Topological Vector Spaces, Addison-Wesley.
B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Gordon and Breach (1967).
D. Amir, “Projections onto continuous function spaces,” Proc. Am. Math. Soc.,15, No. 3, 396–402 (1964).
V. A. Khizhnyak, “On representation of monotone sublinear functionals in terms of the set of their support functionals,” in: Application of Functional Analysis in Approximation Theory [in Russian], Kalinin (1974), pp. 138–143.
Yu. É. Linke, “Sublinear operators with values in spaces of continuous functions,” Dokl. Akad. Nauk SSSR,228, No. 3, 540–542 (1976).
Additional information
Irkutsk, Siberian Energy Institute, Siberian Branch, Academy of Sciences of the USSR. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 1, pp. 139–152, January–February, 1980.
Rights and permissions
About this article
Cite this article
Linke, Y.É. Sublinear operators defined on a cone in a finite-dimensional space. Sib Math J 21, 103–112 (1980). https://doi.org/10.1007/BF00970128
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970128