Examples of \(\mathfrak{KC}\)-maps and \(\mathfrak{KO}\)-maps on topologicalordered spaces
Keywords:
Abstract convex space, KKM theorem, KKM space, mapping classes KCAbstract
We give examples of multimap classes $\mathfrak{KC}$ and $\mathfrak{KO}$ in topological ordered spaces. We obtain generalizations of results of Jeng, Huang, and Zhang [10] and introduce an abstract setting on the KKM theory on ordered spaces as in Park [14].References
N. Bourbaki, Topologie Generale, Paris, Hermann, 1939--1940.
T.-H. Chang and C.-L. Yen, KKM property and fixed point theorems, J. Math. Anal. Appl. 203 (1996), 224--235.
J. Girolo, The Schauder fixed-point theorem for connectivity maps, Colloq. Math. 44 (1981), 59--64.
C. D. Horvath and J. V. Llinares Ciscar, Maximal elements and fixed points for binary relations on topological ordered spaces, J. Math. Econom. 25 (1996), 291--306.
J.-B. Hiriart-Urruty, Images of connected sets by semicontinuous multifunctions, J. Math. Anal. Appl. 111 (1985), 407--422.
W. Kulpa and A. Szymanski, Some remarks on Park's abstract convex spaces, Top. Meth. Nonlinear Anal. 44(2) (2014), 369--379.
S. Lefschetz, Algebraic Topology, Amer. Math. Soc. Colloq. Pub. XXVII, Amer. Math. Soc., New York, 1942.
Q. Luo, KKM and Nash equilibria type theorems in topological ordered spaces, J. Math. Anal. Appl. 264 (2001), 262--269. doi:10.1006/jmaa.2001.7624.
Q. Luo, Ky Fan's section theorem and its applications to topological ordered spaces, Appl. Math. Lett. 17 (2004), 1113--1119.
J.-C. Jeng, Y.-Y. Huang, and H.-L. Zhang, Characterization of maps having the KKM property, Soochow J. Math. 28 (2002), 329--338.
S. Park, On generalizations of the KKM principle on abstract convex spaces, Nonlinear Anal. Forum 11 (2006), 67–-77.
S. Park, Elements of the KKM theory on abstract convex spaces, J. Korean Math. Soc. 45 (1) (2008), 1–-27.
S. Park, Remarks on KC-maps and KO-maps in abstract convex spaces, Nonlinear Anal. Forum 12(1) (2007), 29--40.
S. Park, On the KKM theory of ordered spaces, Linear and Nonlinear Anal. 7(1) (2021), 73--87.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Letters in Nonlinear Analysis and its Applications
This work is licensed under a Creative Commons Attribution 4.0 International License.
