On some optimization problems in not necessarily locally convex space
DOI:
https://doi.org/10.2298/YJOR0802167GKeywords:
set valued mapping, quasi - convex map, non-cooperative equilibriumAbstract
In this note, by using O. Hadžić's generalization of a fixed point theorem of Himmelberg, we prove a non - cooperative equilibrium existence theorem in non - compact settings and a generalization of an existence theorem for non - compact infinite optimization problems, all in not necessarily locally convex spaces.References
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Fan, K., “Fixed point and minimax theorems in locally convex topological linear spaces”, Proc. Math. Acad. Sri. U.S.A., 38 (1952) 121-126.
Hadžić, O., Fixed Point Theory in Topological Vector Spaces, University of Novi Sad, Novi Sad, 1984.
Himmelberg, C.J., “Fixed point of compact multifunctions”, J. Math. Anal. Appl, 38 (1972) 205-207.
Kaczynski, T., and Zeidan, V., “An application of Ky Fan fixed point theorem to an optimization problem”, Nonlinear Anal. TMA, 13 (1989) 259-261.
Im, S.M., and Kim, W.K., “An application of Himmelberg's fixed point theorem to non-compact optimization problems”, Bulletin of the Institute of Mathematics Academia Sinica, 19(2) (1991) 147-151.
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