In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1072, author = {Mircea Balaj}, title = {Constant selections and minimax inequalities}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {26}, year = {2006}, pages = {159-173}, zbl = {1144.54027}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1072} }
Mircea Balaj. Constant selections and minimax inequalities. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 26 (2006) pp. 159-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1072/
[000] [1] J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers 2003. | Zbl 1029.55002
[001] [2] J.P. Aubin and J. Ekeland, Applied Nonlinear Analysis, A Wiley-Interscience Publications, John Wiley & Sons Inc., New York 1984.
[002] [3] M. Balaj, Admissible maps, intersection results, coincidence theorems, Comment. Math. Univ. Carolinae 42 (2001), 753-762. | Zbl 1068.47068
[003] [4] R.C. Bassanezi and G.H. Greco, A minimax theorem for marginally u.s.c./l.s.c. functions, Topol. Methods Nonlinear Anal. 5 (1995), 249-253. | Zbl 0859.49006
[004] [5] C. Berge, Espaces Topologique, Edinburgh, London, Oliver and Boyd 1963.
[005] [6] T.-H. Chang and C.-L. Yen, KKM property and fixed point theorems, J. Math. Anal. Appl. 203 (1996), 224-235. | Zbl 0883.47067
[006] [7] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, 1999. | Zbl 0937.55001
[007] [8] Ky Fan, Sur une théorème minimax, C. R. Acad. Sci. Paris 259 (1964), 3925-3928. | Zbl 0138.37304
[008] [9] Ky Fan, A minimax inequality and its applications, in 'Inequality III' (O. Shisha, ed.), pp.~103-113, Academic Press, New York 1972.
[009] [10] Ky Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. | Zbl 0515.47029
[010] [11] A. Granas and F.-C. Liu, Quelques théorèmes de minimax sans convexité, C. R. Acad. Sci. Paris 300 (1985), 347-350. | Zbl 0573.49008
[011] [12] A. Granas and F.-C. Liu, Coincidences for set-valued maps and minimax inequalities, J. Math. Pures Appl. 65 (1986), 119-148. | Zbl 0659.49007
[012] [13] C.-W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77. | Zbl 0413.47042
[013] [14] C.-W. Ha, On a minimax inequality of Ky Fan, Proc. Am. Math. Soc. 99 (1987), 680-682. | Zbl 0633.47037
[014] [15] L-J. Lin, Applications of a fixed point theorem in G-convex spaces, Nonlinear Anal. 46 (2001), 601-608. | Zbl 1001.47041
[015] [16] F.-C. Liu, A note on the von Neumann-Sion minimax principle, Bull. Inst. Math. Acad. Sinica 6 (1978), 517-524. | Zbl 0421.46006
[016] [17] E. Michael, Continuous selections I, Ann. Math. 63 (2) (1956), 361-381. | Zbl 0071.15902
[017] [18] E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-651. | Zbl 0151.30805
[018] [19] S. Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl. 141 (1989), 164-176. | Zbl 0681.47028
[019] [20] S. Park, Generalized Fan-Browder fixed point theorems and their applications, in 'Collection of Papers Dedicated to J.G. Park', pp. 51-77, 1989.
[020] [21] S. Park, Some coincidence theorems for acyclic multifunctions and applications to KKM theory, in 'Fixed Point Theory and Applications' (K.-K. Tan, Ed.), pp. 248-277, World Scientific, River Edge, New Jersey 1992.
[021] [22] S. Park, Foundations of the KKM via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-519. | Zbl 0829.49002
[022] [23] S. Park, Acyclic versions of the von Neumann and Nash equilibrium theorems, J. Comput. Appl. Math. 113 (2000), 83-91. | Zbl 0947.47039
[023] [24] H.K. Pathak and M.S. Khan, On D-KKM theorem and its applications, Bull. Austral. Math. Soc. 67 (2003), 67-77. | Zbl 1044.47037
[024] [25] M. Sion, On general minimax theorems, Pacific J. Math. 8 (1958), 171-176. | Zbl 0081.11502