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Fixed point theorems for generalized set-contraction maps and their applications. (English) Zbl 1225.54012
Summary: A new generalized set-valued contraction on topological spaces with respect to a measure of noncompactness is introduced. Two fixed point theorems for the KKM type maps which are either generalized set-contraction or condensing ones are given. Furthermore, applications of these results to the existence of coincidence points and maximal elements are deduced.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54C50Special sets of topological spaces defined by functions
47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
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References:
[1] Kuratowski, C.: Sur LES espaces completes, Fund. math. 15, 301-309 (1930) · Zbl 56.1124.04
[2] Akhmerov, R. R.; Kamenskiĭ, M. I.; Potapov, A. S.; Rodkina, A. E.; Sadovskiĭ, B. N.: Measures of noncompactness and condensing operators, (1992) · Zbl 0748.47045
[3] Appell, J.: Measures of noncompactness, condensing operators and fixed points: an application-oriented survey, Fixed point theory 6, No. 2, 157-229 (2005) · Zbl 1102.47041
[4] J.K. Hale, {$\alpha$}-contraction and differential equations, in: Proc. Equations Differential Fon. Nonlin., Brussels, 1975, Hermann, Paris, p. 15042
[5] Hale, J. K.: Theory of functional differential equations, Appl. math. Sci. 3 (1977) · Zbl 0352.34001
[6] Khamsi, M. A.; Kirk, W. A.: An introduction to metric spaces and fixed point theory, (2001) · Zbl 1318.47001
[7] Nussbaum, R. D.: The fixed point index for local condensing maps, Ann. mat. Pura appl. 89, No. 4, 217-258 (1971) · Zbl 0226.47031 · doi:10.1007/BF02414948
[8] Sadovskii, B. N.: On fixed point principle, Funktsional. anal. 4, 74-76 (1967) · Zbl 0165.49102
[9] Darbo, G.: Punti uniti in trasformazioni a codominio non compatto, Rend. sem. Mat. univ. Padova 24, 84-92 (1955) · Zbl 0064.35704 · numdam:RSMUP_1955__24__84_0
[10] Khamsi, M. A.: KKM and Ky Fan theorems in hyperconvex spaces, J. math. Anal. appl. 204, 298-306 (1996) · Zbl 0869.54045 · doi:10.1006/jmaa.1996.0438
[11] Amini, A.; Fakhar, M.; Zafarani, J.: Fixed point theorems for the class S-KKM mappings in abstract convex spaces, Nonlinear anal. 66, No. 1, 14-21 (2007) · Zbl 1116.47046 · doi:10.1016/j.na.2005.11.005
[12] Amini, A.; Fakhar, M.; Zafarani, J.: KKM mappings in metric spaces, Nonlinear anal. 60, 1045-1052 (2005) · Zbl 1076.47043 · doi:10.1016/j.na.2004.10.003
[13] Chang, T. H.; Yen, C. L.: KKM property and fixed point theorems, J. math. Anal. appl. 203, 224-235 (1996) · Zbl 0883.47067 · doi:10.1006/jmaa.1996.0376
[14] Chen, C. M.: KKM property and fixed point theorems in metric spaces, J. math. Anal. appl. 323, 1231-1237 (2006) · Zbl 1110.54023 · doi:10.1016/j.jmaa.2005.11.030
[15] Dhompongsa, S.; Yingtaweesittikul, H.: Diametrically contractive multivalued mappings, Fixed point theory appl., 7 (2007) · Zbl 1171.47044 · doi:10.1155/2007/19745
[16] Khamsi, M. A.: Sadovskii’s fixed point theorem without convexity, Nonlinear anal. 53, 829-837 (2003) · Zbl 1028.47042 · doi:10.1016/S0362-546X(03)00038-5
[17] De Blasi, F.: The measure the weak non compactness of the unit sphere in a Banach space is either zero or one, Ist. mat. Ulissebini 7 (1974--75)
[18] Lopes-Pinto, A. J. B.: Fixed point theorems for ${\beta}$-contractions, Centro mat. Fund. 19 (1979)
[19] Lopes-Pinto, A. J. B.: Fixed point theorems. Ordinary and partial differential equations, Lecture notes in math. 846 (1981)