Admissible maps, intersection results, coincidence theorems

Mircea Balaj

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 4, page 753-762
  • ISSN: 0010-2628

Abstract

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We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.

How to cite

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Balaj, Mircea. "Admissible maps, intersection results, coincidence theorems." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 753-762. <http://eudml.org/doc/248812>.

@article{Balaj2001,
abstract = {We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.},
author = {Balaj, Mircea},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {acyclic map; convex space; matching theorem; coincidence theorem; acyclic map; convex space; matching theorem; coincidence theorem},
language = {eng},
number = {4},
pages = {753-762},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Admissible maps, intersection results, coincidence theorems},
url = {http://eudml.org/doc/248812},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Balaj, Mircea
TI - Admissible maps, intersection results, coincidence theorems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 4
SP - 753
EP - 762
AB - We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.
LA - eng
KW - acyclic map; convex space; matching theorem; coincidence theorem; acyclic map; convex space; matching theorem; coincidence theorem
UR - http://eudml.org/doc/248812
ER -

References

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  1. Allen G., Variational inequalities, complementary problems and duality theorems, J. Math. Anal. Appl. 58 (1977), 1-10. (1977) MR0513305
  2. Balaj M., A variant of a fixed point theorem of Browder and some applications, Math. Montisnigri 9 (1998), 5-13. (1998) Zbl0999.47045MR1657668
  3. Ben-El-Mechaiekh H., Deguire P., Granas A., Points fixes et coincidences pour les applications multivoque, I , C.R. Acad. Sci. Paris 295 (1982), 337-340; II, 381-384. (1982) 
  4. Browder F.E., The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-301. (1968) Zbl0176.45204MR0229101
  5. Chang S.Y., A generalization of KKM principle and its applications, Soochow J. Math. 15 (1989), 7-17. (1989) Zbl0747.47033MR1025967
  6. Ding X.-P., Tan K.-K., Matching theorems, fixed point theorems, and minimax inequalities without convexity, J. Austral. Math. Soc. (Ser. A) 49 (1990), 111-128. (1990) Zbl0709.47053MR1054086
  7. Fan K., A generalization of Tychonoff's fixed point theorem, Math. Ann 142 (1961), 305-310. (1961) Zbl0093.36701MR0131268
  8. Fan K., A minimax inequality and applications, in ``Inequalities III'', O Shisha (ed.), Academic Press, New York, 1972, pp.103-113. Zbl0302.49019MR0341029
  9. Fan K., Fixed-point and related theorems for non-compact convex sets, in ``Game Theory and Related Topics'', O. Moeschlin and D. Pallaschke (eds.), North-Holland, Amsterdam, 1979, pp.151-156. Zbl0432.54040MR0556363
  10. Fan K., Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. (1984) Zbl0515.47029MR0735533
  11. Gorniewicz L., A Lefschetz-type fixed point theorem, Fund. Math. 88 (1975), 103-115. (1975) Zbl0306.55007MR0391062
  12. Gorniewicz L., Homological methods in fixed point theory of multi-valued maps, Dissertationes Math. 129 (1976), 1-71. (1976) Zbl0324.55002MR0394637
  13. Ha C.-W., Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77. (1980) Zbl0413.47042MR0569411
  14. Kim W.K., Some applications of the Kakutani fixed point theorem, J. Math. Anal. Appl. 121 (1987), 119-122. (1987) Zbl0612.54055MR0869523
  15. Lassonde M., On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201. (1983) Zbl0527.47037MR0721236
  16. Lassonde M., Sur le principle KKM, C.R. Acad. Sci. Paris 310 (1990), 573-576. (1990) MR1050134
  17. Lin T.-C., Convex sets, fixed points, variational and minimax inequalities, Bull. Austral. Math. Soc. (Ser. A) 34 (1986), 107-117. (1986) Zbl0597.47038MR0847978
  18. Park S., Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl. 141 (1989), 164-176. (1989) Zbl0681.47028MR1004591
  19. Park S., Convex spaces and KKM families of subsets, Bull. Korean Math. Soc. 27 (1990), 11-14. (1990) Zbl0746.47036MR1060811
  20. Park S., Generalizations of Ky Fan’s matching theorems and their applications, I I , J. Korean Math. Soc. 28 (1991), 275-283. (1991) Zbl0813.47063MR1127832
  21. Park S., Some coincidence theorems on acyclic multifunctions and applications to KKM theory, in ``Fixed Point Theory and Applications'' (K.-K. Tan ed.), World Scientific, Publishing River Edge, NY, 1992, pp.248-277. MR1190044
  22. Park S., Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-519. (1994) Zbl0829.49002MR1297433
  23. Park S., Ninety years of the Browder fixed point theorem, Vietnam J. Math. 27 (1999), 193-232. (1999) MR1811334
  24. Park S., Kim H., Coincidences of composites of u.s.c. maps on H -spaces and applications, J. Korean Math. Soc. 32 (1995), 251-264. (1995) Zbl0868.54015MR1338994
  25. Sehgal V.M., Singh S.P., Whitfield J.H.M., KKM-maps and fixed point theorems, Indian J. Math. 32 (1990), 289-296. (1990) MR1088610
  26. Shih M.-H., Covering properties of convex sets, Bull. London Math. Soc. 18 ((1986)), 57-59. ((1986)) Zbl0579.52004MR0841369
  27. Shih M.-H., Tan K.-K., Covering theorems of convex sets related to fixed-point theorems, in ``Nonlinear and Convex Analysis-Proc. in Honor of Ky Fan'' (B-L. Lin and S. Simons, eds.), Marcel Dekker, New York, 1987, pp.235-244. Zbl0637.47029MR0892795
  28. Shih M.-H., Tan K.K., A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems, J. Austral. Math. Soc. 45 (1988), 169-183. (1988) Zbl0664.52001MR0951575
  29. Shioji N., A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorems, Proc. Amer. Math. Soc. 111 (1991), 187-195. (1991) MR1045601
  30. Takahashi W., Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), 168-181. (1976) Zbl0314.47032MR0399979
  31. Tarafdar E., On nonlinear variational inequalities, Proc. Amer. Math. Soc. 67 (1977), 95-98. (1977) Zbl0369.47029MR0467408
  32. Tarafdar E., On minimax principles and sets with convex sections, Publ. Math. Debrecen 29 (1982), 219-226. (1982) Zbl0536.47038MR0678897

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