The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications
George Isac; George Xian-Zhi Yuan
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1999)
- Volume: 19, Issue: 1-2, page 17-33
- ISSN: 1509-9407
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] P. Alexandroff and B. Pasynkoff, Elementary proof of the essentiality of the identical mapping of a simplex (in Russian), Uspehi Mat. Nauk (N.S.) 12 (1957), 175-179.
- [2] N. Aronszajn and P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439. Zbl0074.17802
- [3] C. Bardaro and R. Ceppitelli, Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities, J. Math. Anal. Appl. 132 (1988), 484-490. Zbl0667.49016
- [4] F.E. Browder, The fixed point theory of multivalued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-301. Zbl0176.45204
- [5] S.S. Chang and Y. Zhang, Generalized KKM theorem and variational inequalities, J. Math. Anal. Appl. 159 (1993), 208-223. Zbl0739.47026
- [6] X.P. Ding and K.K. Tan, A minimax inequality with applications to existence of equilibrium points and fixed point theorems, Coll. Math. 68 (1992), 233-247. Zbl0833.49009
- [7] J. Dugundji and A. Granas, Fixed Point Theory 1, PWN Warszawa 1982.
- [8] K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310. Zbl0093.36701
- [9] K. Fan, Extensions of two fixed point theorems of F.E. Browder, Math. Z. 112 (1969), 234-240. Zbl0185.39503
- [10] K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. Zbl0515.47029
- [11] A. Granas, KKM-maps and their applications to nonlinear problems, The Scottish Book: Mathematics from the Scottish Cafe ed., R. Daniel Mauldin, Birkhäuser, Boston (1982) 45-61.
- [12] C. Horvath, Contractibility and generalized convexity, J. Math. Anal. Appl. 156 (1991) 341-357. Zbl0733.54011
- [13] J.R. Isbell, Six theorems about injective metric spaces, Comm. Math. Helvetici 39 (1964), 65-76. Zbl0151.30205
- [14] J.L. Kelley, Banach spaces with the extension property, Trans. Amer. Math. Soc. 72 (1952), 323-326. Zbl0046.12002
- [15] M.A. Khamsi, KKM and Ky Fan theorems in hyperconvex metric spaces, J. Math. Anal. Appl. 204 (1996), 298-306. Zbl0869.54045
- [16] B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für n-dimensional simplexe, Fund. Math. 14 (1929), 132-137. Zbl55.0972.01
- [17] W.K. Kim, Some applications of the Kakutani fixed point theorems, J. Math. Anal. Appl. 121 (1987), 119-122. Zbl0612.54055
- [18] W.A. Kirk and S.S. Shin, Fixed point theorems in hyperconvex spaces, Houston J. Math. 23 (1997), 175-187. Zbl0957.46033
- [19] W.A. Kirk, B. Sims and X.Z. Yuan, The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications, Nonlinear Anal., T.M.A. (in press) (1999). Zbl1068.47072
- [20] V.L. Klee, On certain intersection properties of convex sets, Canad. J. Math. 3 (1951), 272-275. Zbl0042.40701
- [21] H.E. Lacey, The Isometric Theory of Classical Banach Spaces, Springer Verlag, New York 208 (1974). Zbl0285.46024
- [22] M. Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201. Zbl0527.47037
- [23] M. Lassonde, Sur le principle KKM, C.R. Acad. Sci. Paris. Série I. 310 (1990), 573-576. Zbl0715.47038
- [24] M. Lin and R.C. Sine, Retractions on the fixed point set of semigroup of nonexpansive maps in hyperconvex spaces, Nonlinear Anal., T.M.A. 15 (1990), 943-954. Zbl0747.47045
- [25] L. Nachbin, A theorem of Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1960), 28-54.
- [26] S. Park, Some coincidence theorems on acyclic multifunctions and applications to KKM theory, Fixed Point Theory and Applications, Ed. K.K. Tan, World Scientific, Singapore (1992), 248-278.
- [27] S. Park, Fixed point theorems in hyperconvex metric spaces, Nonlinear Anal., T.M.A. 37 (1999), 467-472. Zbl0930.47023
- [28] M.H. Shih, Covering properties of convex sets, Bull. London Math. Soc. 18 (1986), 57-59. Zbl0579.52004
- [29] M.H. Shih and K.K. Tan, Covering theorems of convex sets related to fixed-point theorems, Nonlinear Analysis and Convex Analysis, Eds. B.L. Lin and S. Simons, Marcel Dekker Inc., New York and Basel (1987) 235-244.
- [30] R.C. Sine, On nonlinear contraction semigroups in Sup-norm spaces, Nonlinear Anal., T.M.A. 3 (1979), 885-890. Zbl0423.47035
- [31] R.C. Sine, Hyperconvexity and nonexpansive multifunctions, Trans. Amer. Math. Soc. 315 (1989), 755-767. Zbl0682.47029
- [32] R.C. Sine Hyperconvexity and approximate fixed points, Nonlinear Anal., T.M.A. 13 (1989), 863-869. Zbl0694.54033
- [33] P.M. Soardi, Existence of fixed points of nonexpansinve mappings in certain Banach lattices, Proc. Amer. Math. Soc. 73 (1979), 25-29. Zbl0371.47048
- [34] E. Tarafdar, A fixed point theorem equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorem, J. Math. Anal. Appl. 128 (1987), 475-479. Zbl0644.47050
- [35] G.X.Z. Yuan, Fixed points of upper semicontinuous mappings in locally G-convex spaces, Bull. Austral. Math. Soc. 58 (1998), 469-478. Zbl0927.47034
- [36] G.X.Z. Yuan, KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker, New York 1999.
- [37] E. Zeidler, Nonlinear Functional Analysis and Its Applications I: Fixed Point Theorems, Springer Verlag, New York 1986. Zbl0583.47050