Constant selections and minimax inequalities

Mircea Balaj

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2006)

  • Volume: 26, Issue: 1, page 159-173
  • ISSN: 1509-9407

Abstract

top
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.

How to cite

top

Mircea 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. [1] J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers 2003. Zbl1029.55002
  2. [2] J.P. Aubin and J. Ekeland, Applied Nonlinear Analysis, A Wiley-Interscience Publications, John Wiley & Sons Inc., New York 1984. 
  3. [3] M. Balaj, Admissible maps, intersection results, coincidence theorems, Comment. Math. Univ. Carolinae 42 (2001), 753-762. Zbl1068.47068
  4. [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. [5] C. Berge, Espaces Topologique, Edinburgh, London, Oliver and Boyd 1963. 
  6. [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. [7] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, 1999. Zbl0937.55001
  8. [8] Ky Fan, Sur une théorème minimax, C. R. Acad. Sci. Paris 259 (1964), 3925-3928. Zbl0138.37304
  9. [9] Ky Fan, A minimax inequality and its applications, in 'Inequality III' (O. Shisha, ed.), pp.~103-113, Academic Press, New York 1972. 
  10. [10] Ky Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. Zbl0515.47029
  11. [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. [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. [13] C.-W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77. Zbl0413.47042
  14. [14] C.-W. Ha, On a minimax inequality of Ky Fan, Proc. Am. Math. Soc. 99 (1987), 680-682. Zbl0633.47037
  15. [15] L-J. Lin, Applications of a fixed point theorem in G-convex spaces, Nonlinear Anal. 46 (2001), 601-608. Zbl1001.47041
  16. [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. [17] E. Michael, Continuous selections I, Ann. Math. 63 (2) (1956), 361-381. Zbl0071.15902
  18. [18] E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-651. Zbl0151.30805
  19. [19] S. Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl. 141 (1989), 164-176. Zbl0681.47028
  20. [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. [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. [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. [23] S. Park, Acyclic versions of the von Neumann and Nash equilibrium theorems, J. Comput. Appl. Math. 113 (2000), 83-91. Zbl0947.47039
  24. [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. [25] M. Sion, On general minimax theorems, Pacific J. Math. 8 (1958), 171-176. Zbl0081.11502

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.