Constant selections and minimax inequalities
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 26 (2006) no. 1, pp. 159-173.

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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.
Keywords: map, constant selection, acyclic map, matching theorem, analytic alternative, minimax inequality
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Balaj, Mircea. Constant selections and minimax inequalities. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 26 (2006) no. 1, pp. 159-173. http://geodesic.mathdoc.fr/item/DMDICO_2006_26_1_a9/

[1] J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers 2003.

[2] J.P. Aubin and J. Ekeland, Applied Nonlinear Analysis, A Wiley-Interscience Publications, John Wiley Sons Inc., New York 1984.

[3] M. Balaj, Admissible maps, intersection results, coincidence theorems, Comment. Math. Univ. Carolinae 42 (2001), 753-762.

[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.

[5] C. Berge, Espaces Topologique, Edinburgh, London, Oliver and Boyd 1963.

[6] T.-H. Chang and C.-L. Yen, KKM property and fixed point theorems, J. Math. Anal. Appl. 203 (1996), 224-235.

[7] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, 1999.

[8] Ky Fan, Sur une théorème minimax, C. R. Acad. Sci. Paris 259 (1964), 3925-3928.

[9] Ky Fan, A minimax inequality and its applications, in 'Inequality III' (O. Shisha, ed.), pp.~103-113, Academic Press, New York 1972.

[10] Ky Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537.

[11] A. Granas and F.-C. Liu, Quelques théorèmes de minimax sans convexité, C. R. Acad. Sci. Paris 300 (1985), 347-350.

[12] A. Granas and F.-C. Liu, Coincidences for set-valued maps and minimax inequalities, J. Math. Pures Appl. 65 (1986), 119-148.

[13] C.-W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77.

[14] C.-W. Ha, On a minimax inequality of Ky Fan, Proc. Am. Math. Soc. 99 (1987), 680-682.

[15] L-J. Lin, Applications of a fixed point theorem in G-convex spaces, Nonlinear Anal. 46 (2001), 601-608.

[16] F.-C. Liu, A note on the von Neumann-Sion minimax principle, Bull. Inst. Math. Acad. Sinica 6 (1978), 517-524.

[17] E. Michael, Continuous selections I, Ann. Math. 63 (2) (1956), 361-381.

[18] E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-651.

[19] S. Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl. 141 (1989), 164-176.

[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.

[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.

[22] S. Park, Foundations of the KKM via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-519.

[23] S. Park, Acyclic versions of the von Neumann and Nash equilibrium theorems, J. Comput. Appl. Math. 113 (2000), 83-91.

[24] H.K. Pathak and M.S. Khan, On D-KKM theorem and its applications, Bull. Austral. Math. Soc. 67 (2003), 67-77.

[25] M. Sion, On general minimax theorems, Pacific J. Math. 8 (1958), 171-176.