30
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

A united approach to generalization of the KKM-type theorems related to acyclic maps

Pages 105-119 | Received 10 Jul 1992, Accepted 16 Jul 1993, Published online: 15 May 2007

References

  • Bardaro , C. and Ceppitelli , R. 1988 . Some further generalizations of Knaster-Kura-towski-Mazurkiewicz theorem and minimax inequalities . J. Math. Anal. Appl , 132 : 484 – 490 .
  • Bardaro , C. and Ceppitelli , R. 1989 . Applications of the generalized Knaster-Kuratowski-Mazurkiewicz theorem to variational inequalities . J. Math. Anal. Appl , 137 : 46 – 58 .
  • Bardaro , C. and Ceppitelli , R. 1982 . Fixed point theorems and vector-valued minimax theorems . J. Math. Anal.Appl , 146 : 337 – 340 .
  • Ben-El-Mechaiekh , H. , Deguire et , P. and Granas , A. 1982 . Points fixes et coincidences pour las applications multivoque (applications de Ky Fan) . C. R. Acad. Sci. Paris , 295 : 337 – 340 .
  • Bielawski , R. 1987 . Simplicial convexity and its applications . J. Math. Anal. Appl , 127 : 155 – 171 .
  • Brézis , H. , Nirenberg , L. and Stampacchia , G. 1972 . A remark on Ky Fan's minimax principle . Boll. Un. Mat. Ital , 6 : 293 – 300 .
  • Chang , S.S. and Zhang , Y. 1991 . Generalized KKM theorem and variational inequalities . J. Math. Anal. Appl , 159 : 208 – 223 .
  • Chang , S.Y. 1989 . A generalization of KKM principle and its applications . Soochow J.Math , 15 : 7 – 17 .
  • Ding , X.P. and Tan , K.K. 1990 . Matching theorems, fixed point theorems, and minimax inequalities without convexity . J. Austral. Math. Soc , A49 : 111 – 128 .
  • Ding , X.P. , Kim , W.K. and Tan , K.K. 1990 . A new minimax inequality on H-spaces with applications . Bull. Austral. Math. Soc , 41 : 457 – 473 .
  • Ding , X.P. , Kim , W.K. and Tan , K.K. 1990 . Applications of a minimax inequality on H-spaces . Bull. Austral. Math.Soc , 41 : 475 – 485 .
  • Dugundji , J. and Granas , A. 1978 . KKM-maps and variational inequalities . Ann. Scuola Norm. Sup. Pisa , 5 : 679 – 682 .
  • Fan , Ky . 1961 . A generalization of Tychonoff's fixed point theorem . Math. Ann , 142 : 305 – 310 .
  • Fan , Ky . 1969 . Extensions of two fixed point theorems of F.E. Browder . Math. Z , 112 : 234 – 240 .
  • Fan , Ky . 1972 . “ A minimax inequality and applications ” . In Inequalities III , Edited by: Shisha , O. 103 – 113 . New York : Academic Press .
  • Fan , Ky . 1979 . “ Fixed-point and related theorems for non-compact convex sets ” . In Game Theory and Related Topics , Edited by: Moeschlin , O. and Pallaschke , D. 151 – 156 . Amsterdam : North-Holland Publ. Co .
  • Fan , Ky . 1981 . “ A further generalization of Shapley's generalization of the Knaster-Kur-atowski-Mazurkiewicz theorem ” . In in Game Theory and Mathematical Economics , Edited by: Moeschlin , O. and Palaschke , D. 275 – 279 . Amsterdam : North-Holland Publ. Co .
  • Fan , Ky . 1984 . Some properties of convex sets related to fixed point theorems . Math.Ann , 266 : 519 – 537 .
  • Granas , A. 1981 . “ KKM-maps and their applications to nonlinear problems ” . In The Scottish book , Edited by: Mauldin , R.D. 45 – 61 . Boston : Birkhäuser .
  • Granas , A. 1990 . “ Sur quélques methodes topologique en analyse convexe ” . In Sém. Math.Super , Vol. 110 , 11 – 77 . Pres. Univ. Montréal .
  • Guillerme , J. 1991 . “ Les inégalités “Inf-Sup ≤ Sup-Inf,” . In Fixed point theory and applications , Edited by: Théra , M.A. and Baillon , J.B. 193 – 214 . Essex : Longman Scientific & Technical .
  • Ha , C.W. 1980 . Minimax and fixed point theorems . Math. Ann , 248 : 73 – 77 .
  • Horvath , C.D. 1983 . Points fixes et coincidences pour les applications multivoques sans convexité . C. R. Acad. Sci. Paris , 296 : 403 – 406 .
  • Horvath , C.D. 1983 . Points fixes et coincidences dans les espaces topologiques compacts contractibles . C. R. Acad. Sci. Paris , 296 : 403 – 406 .
  • Horvath , C.D. 1987 . “ Some results on multivalued mappings and inequalities without convexity ” . In in Nonlinear and convex analysis—Proc. in honor of Ky Fan , Edited by: Lin , B.L. and Simons , S. 99 – 106 . New York : Marcel Dekker .
  • Horvath , C.D. 1990 . “ Convexité généralisée et applications ” . In Sém. Math. Super. , Vol. 110 , 79 – 99 . Pres. Univ.Montréal .
  • Horvath , C.D. 1991 . Contractibility and generalized convexity . J. Math. Anal. Appl , 156 : 341 – 357 .
  • Ichiishi , T. 1981 . On the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem . J. Math.Anal. Appl , 81 : 297 – 299 .
  • Ichiishi , T. 1988 . Alternative version of Shapley's theorem on closed coverings of a simplex . Proc. Amer. Math. Soc , 104 : 759 – 763 .
  • Ichiishi , T. and Idzik , A. 1990 . Theorems on closed coverings of a simplex and their applications to cooperative game theory . J. Math. Anal. Appl , 146 : 259 – 270 .
  • Jiang , J. 1990 . Coincidence theorems and minimax theorems . Acta Math. Sinica , 5 : 307 – 320 .
  • Kim , W.K. 1987 . Some applications of the Kakutani fixed point theorem . J. Math. Anal.Appl , 121 : 119 – 122 .
  • Kim , W.K. 1987 . Some intersection theorems of the KKM-maps . Bull. Korean Math. Soc , 24 : 139 – 144 .
  • Knaster , B. , Kuratowski , K. and Mazurkiewicz , S. 1929 . Bin Beweis des Fixpunktsatzes fur n-dimensionale Simplexe . Fund. Math , 14 : 132 – 137 .
  • Lassonde , M. 1983 . On the use of KKM multifunctions in fixed point theory and related topics . J. Math. Anal. Appl , 97 : 151 – 201 .
  • Lassonde , M. 1990 . Sur le principe KKM . C. R. Acad. Sci. Paris , 310 : 573 – 576 .
  • Lin , T.C. 1986 . Convex sets, fixed points, variational and minimax inequalities . Bull.Austral. Math. Soc , 34 : 107 – 117 .
  • Liu , F.C. 1991 . On a form of KKM principle and SupInfSup inequalities of von Neumann and of Ky Fan type . J. Math. Anal. Appl , 155 : 420 – 436 .
  • Park , Sehie . 1989 . Generalized Fan-Browder fixed point theorems and their applications . Collec. of Papers Dedicated to J.G. Park , 155 : 51 – 77 .
  • Park , Sehie . 1989 . Generalizations of Ky Fan's matching theorems and their applications . J.Math. Anal. Appl , 141 : 164 – 176 .
  • Park , Sehie . 1990 . Generalized matching theorems for closed coverings of convex sets . Numer. Funct. Anal, and Optimiz , 11 : 101 – 110 .
  • Park , Sehie . 1991 . Generalizations of Ky Fan's matching theorems and their applications . II, J. Korean Math. Soc , 28 : 275 – 283 .
  • Park , Sehie . 1990 . Convex spaces and KKM families of subsets . Bull. Korean Math. Soc , 27 : 11 – 14 .
  • Park , Sehie . Some coincidence theorems on acyclic multifunctions and applications to KKM theory . Proc. 2nd Int. Conf. on Fixed Point Theory and Applications . June 9–14 1991 , Halifax. Edited by: Tan , K.K. pp. 248 – 277 . River Edge, NJ : World Scientific .
  • Park , Sehie . 1993 . On the KKM type theorems on spaces having certain contractible subsets . Kyungpook Math. J , 32 : 607 – 628 .
  • Park , Sehie . 1993 . On minimax inequalities on spaces having certain contractible subsets . Bull. Austral. Math. Soc , 47 : 25 – 40 .
  • Sehgal , V.M. , Singh , S.P. and Whitfield , J.H.M. 1990 . KKM-maps and fixed point theorems . Indian J. Math , 32 : 289 – 296 .
  • Shapley , L.S. 1973 . “ On balanced games without side payments ” . In in Mathematical Programming , Edited by: Hu , T.C. and Robinson , S.M. 261 – 290 . New York : Academic Press .
  • Shih , M.H. 1986 . Covering properties of convex sets . Bull. London Math. Soc , 18 : 57 – 59 .
  • Shih , M.H. and Tan , K.K. 1985 . “ The Ky Fan minimax principle, sets with convex sections, and variational inequalities ” . In Differential Geometry, Calculus of Variations and Their Applications , Edited by: Rassias , G.M. and Rassias , T.M. 471 – 481 . New York : Marcel Dekker .
  • Shih , M.H. and Tan , K.K. 1986 . Minimax inequalities and applications . Contemp. Math , 54 : 45 – 63 .
  • Shih , M.H. and Tan , K.K. 1986 . Covering theorems of simplexes and systems of linear inequalities . Linear and Multilinear Algebra , 19 : 309 – 320 .
  • Shih , M.H. and Tan , K.K. 1987 . “ Covering theorems of convex sets related to fixed-point theorems ” . In Nonlinear and convex analysis—Proc. in honor of Ky Fan , Edited by: Lin , B.L. and Simons , S. 235 – 244 . New York : Marcel Dekker .
  • Shih , M.H. and Tan , K.K. 1987 . “ Shapley selections and covering theorems of simplexes ” . In Nonlinear and convex analysis—Proc. in honor of Ky Fan , Edited by: Lin , B.L. and Simons , S. 245 – 251 . New York : Marcel Dekker .
  • Shih , M.H. and Tan , K.K. 1988 . A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems . J. Austral. Math. Soc. , 45 : 169 – 183 .
  • Shioji , N. 1991 . A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem . Proc. Amer. Math. Soc , 111 : 187 – 195 .
  • Simons , S. 1986 . On existence theorem for quasiconcave functions with applications, . Nonlinear Anal. TMA. , 10 : 1133 – 1152 .
  • Takahashi , W. 1976 . Nonlinear variational inequalities and fixed point theorems . J.Math. Soc. Japan , 28 : 168 – 181 .
  • Tarafdar , E. 1982 . On minimax principles and sets with convex sections . Publ. Math.Debrecen , 29 : 219 – 226 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.