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http://dx.doi.org/10.22771/nfaa.2021.26.01.07

COLLECTIVE FIXED POINTS FOR GENERALIZED CONDENSING MAPS IN ABSTRACT CONVEX UNIFORM SPACES  

Kim, Hoonjoo (Department of Mathematics Education Sehan University)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.1, 2021 , pp. 93-104 More about this Journal
Abstract
In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.
Keywords
Abstract convex space; KKM map; $L{\Gamma}$-space; the Zima type; KC-map; KKM space; generalized condensing map; ${\Phi}$-map; S-KKM map; better admissible class B; fixed point;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 R.P. Agarwal and D. O'Regan, Fixed points, morphisms, countably condensing pairs and index theory, Nonlinear Funct. Anal. Appl., 7(2) (2002), 241-253.
2 A. Amini-Harandi, A.P. Farajzadeh, D. O'Regan and R.P. Agarwal, Fixed point theorems for condensing multimaps on abstract convex uniform spaces, Nonlinear Funct. Anal. Appl., 14 (2009), 109-120.
3 T.-H. Chang, Y.-Y. Huang, J.-C. Jeng and K.-H. Kuo, On S-KKM property and related topics, J. Math. Anal. Appl., 229 (1999), 212-227.   DOI
4 C.J. Himmelberg, J. R. Porter and F.S. Van Vleck, Fixed point theorems for condensing multifunctions, Proc. Amer. Math. Soc., 23 (1969), 635-641.   DOI
5 Y.-Y. Huang, J.-C. Jeng and T.-Y. Kuo, Fixed point theorems for condensing maps in S-KKM class, Int. J. Math. Anal., 2 (2008), 1031-1044.
6 Y.-Y. Huang, T.-Y. Kuo and J.-C. Jeng, Fixed point theorems for condensing multimaps on locally G-convex spaces, Nonlinear Anal., 67 (2007), 1522-1531.   DOI
7 H. Kim, Fixed points for generalized condensing maps in abstract convex uniform spaces, Int. J. Math. Anal., 8 (2014), 2899-2908.   DOI
8 S. Park, Elements of the KKM theory on abstract convex spaces, J. Korean Math. Soc., 45 (2008), 1-27.   DOI
9 H. Kim, Maximal elements of condensing maps on abstract convex spaces with applications, J. Nonlinear convex Anal., 20 (2019), 123-131.
10 S. Park, Fixed point theorems in locally G-convex spaces, Nonlinear Anal., 48 (2002), 869-879.   DOI
11 S. Park, Equilibrium existence theorems in KKM spaces, Nonlinear Anal., 69 (2008), 4352-4364.   DOI
12 S. Park, Fixed point theory of multimaps in abstract convex uniform spaces, Nonlinear Anal., 71 (2009), 2468-2480.   DOI
13 S. Park, The KKM principle in abstract convex spaces: equivalent formulations and applications, Nonlinear Anal., 73 (2010), 1028-1042.   DOI
14 S. Park and H. Kim, Admissible classes of multifunctions on generalized convex spaces, Proc. Coll. Natur. Sci., Seoul Nat. Univ., 18 (1993), 1-21.
15 S. Park and H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl., 197 (1996), 173-187.   DOI
16 S. Park and H. Kim, Foundations of the KKM theory on generalized convex spaces, J. Math. Anal. Appl., 209 (1997), 551-571.   DOI
17 W.V. Petryshyn and P.M. Fitzpatrick, Fixed-point theorems for multivalued noncompact inward maps, J. Math. Anal. Appl., 46 (1974), 756-767.   DOI
18 Y-L. Wu, C.-H. Huang and L.-J. Chu, An extension of Mehta theorem with applications, J. Math. Anal. Appl., 391 (2012), 489-495.   DOI