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. (1952) Fixed point and Minimax theorems in locally convex topological linear spaces. Proc Natl Acad Sci USA, vol. 38, str. 121-126
Hadžić, O.L. (1984) Fixed point theory in topological vector spaces. Novi Sad: University of Novi Sad
Himmelberg, C.J. (1972) Fixed points of compact multifunctions. Journal of Mathematical Analysis and Applications, 38(1): 205
Im, S.M., Kim, W.K. (1991) An application of Himmelberg's fixed point theorem to not - compact optimization problems'. Bulletin of the Institute of Mathematics Academia Sinica, 19(2) 147-151
Kaczynski, T., Zeidan, V. (1989) An application of Ky-fan fixed point theorem to an optimization problem. Nonlinear Analysis, 13(3): 259
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