Abstract
In this paper we use new coincidence theorems of the author to obtain a variety of Ky Fan matching type theorems for open coverings related to the map or maps. To establish our new matching results, we consider maps which are of KKM or BPK type (these include the Kakutani maps, the acyclic maps and more generally the admissible maps of Gorniewicz) together with maps which generate HLPY type maps.
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References
C.D. Aliprantis and K.C. Border, Infinite dimensional analysis, Springer Verlag, Berlin, 1994.
H. Ben-El-Mechaiekh, P. Deguire and A. Granas, Points fixes et coincidences pour les applications multivoques II (Applications de type \(\Phi \) and \(\Phi ^{\star }\)), C.R. Acad. Sc., 295(1982), 381–384.
T.H. Chang, Y.Y. Huang, J.C. Jeng and T.H. Chang and K.H. Kuo, On \(S\)–KKM property and related topics, Jour. Math. Anal. Appl., 229(1999), 212–227.
T.H. Chang and C.L. Yen, KKM property and fixed point theorems, Jour. Math. Anal. Appl., 203(1996), 224–235.
X.P. Ding, W.K. Kim and K.K. Tan, A selection theorem and its applications, Bulletin Australian Math. Soc., 46(1992), 205–212.
L. Gorniewicz, Topological fixed point theory of multivalued mappings, Kluwer Acad. Publishers, Dordrecht, 1991.
L. Gorniewicz and M. Slosarski, Topological essentiality and differential inclusions, Bull. Austral. Math. Soc., 45(1992), 177–193.
L.J. Lim, S. Park and Z.T. Yu, Remarks on fixed points, maximal elements and equilibria of generalized games, Jour. Math. Anal. Appl., 233(1999), 581–596.
D. O’Regan, Coincidence results and Leray–Schauder alternatives between multivalued maps with continuous selections and admissible maps, Topology and its Applications, 284(2020), Art. No. 107368, 6pp.
D. O’Regan, KKM type maps and collectively coincidence theory, submitted.
D. O’Regan, Coincidence theory for better admissible multifunctions, Journal of Analysis, to appear.
D.O’Regan and J. Peran, Fixed points for better admissible multifunctions on proximity spaces, Jour. Math. Anal. Appl., 380(2011), 882–887.
S. Park, Coincidence theorems for the better admissible multimaps and their applications, Nonlinear Anal. , 30(1997), 4183–4191.
N.C. Yanelis and N.D. Prabhakar, Existence of maximal elements and equlibria in linear topological spaces, J. Math. Econom., 12(1983), 233–245.
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Communicated by B V Rajarama Bhat.
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O’Regan, D. Intersection results for general classes of maps. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00559-7
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DOI: https://doi.org/10.1007/s13226-024-00559-7