Constant selections and minimax inequalities
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2006)
- Volume: 26, Issue: 1, page 159-173
- ISSN: 1509-9407
Access Full Article
topAbstract
topHow to cite
topMircea Balaj. "Constant selections and minimax inequalities." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 26.1 (2006): 159-173. <http://eudml.org/doc/271190>.
@article{MirceaBalaj2006,
abstract = {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.},
author = {Mircea Balaj},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {map; constant selection; acyclic map; matching theorem; analytic alternative; minimax inequality},
language = {eng},
number = {1},
pages = {159-173},
title = {Constant selections and minimax inequalities},
url = {http://eudml.org/doc/271190},
volume = {26},
year = {2006},
}
TY - JOUR
AU - Mircea Balaj
TI - Constant selections and minimax inequalities
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2006
VL - 26
IS - 1
SP - 159
EP - 173
AB - 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.
LA - eng
KW - map; constant selection; acyclic map; matching theorem; analytic alternative; minimax inequality
UR - http://eudml.org/doc/271190
ER -
References
top- [1] J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers 2003. Zbl1029.55002
- [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. Zbl1068.47068
- [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. Zbl0859.49006
- [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. Zbl0883.47067
- [7] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, 1999. Zbl0937.55001
- [8] Ky Fan, Sur une théorème minimax, C. R. Acad. Sci. Paris 259 (1964), 3925-3928. Zbl0138.37304
- [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. Zbl0515.47029
- [11] A. Granas and F.-C. Liu, Quelques théorèmes de minimax sans convexité, C. R. Acad. Sci. Paris 300 (1985), 347-350. Zbl0573.49008
- [12] A. Granas and F.-C. Liu, Coincidences for set-valued maps and minimax inequalities, J. Math. Pures Appl. 65 (1986), 119-148. Zbl0659.49007
- [13] C.-W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77. Zbl0413.47042
- [14] C.-W. Ha, On a minimax inequality of Ky Fan, Proc. Am. Math. Soc. 99 (1987), 680-682. Zbl0633.47037
- [15] L-J. Lin, Applications of a fixed point theorem in G-convex spaces, Nonlinear Anal. 46 (2001), 601-608. Zbl1001.47041
- [16] F.-C. Liu, A note on the von Neumann-Sion minimax principle, Bull. Inst. Math. Acad. Sinica 6 (1978), 517-524. Zbl0421.46006
- [17] E. Michael, Continuous selections I, Ann. Math. 63 (2) (1956), 361-381. Zbl0071.15902
- [18] E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-651. Zbl0151.30805
- [19] S. Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl. 141 (1989), 164-176. Zbl0681.47028
- [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. Zbl0829.49002
- [23] S. Park, Acyclic versions of the von Neumann and Nash equilibrium theorems, J. Comput. Appl. Math. 113 (2000), 83-91. Zbl0947.47039
- [24] H.K. Pathak and M.S. Khan, On D-KKM theorem and its applications, Bull. Austral. Math. Soc. 67 (2003), 67-77. Zbl1044.47037
- [25] M. Sion, On general minimax theorems, Pacific J. Math. 8 (1958), 171-176. Zbl0081.11502
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.