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Fixed point theorems for weakly contractive multivalued maps. (English) Zbl 1033.47038
The concept of a weakly contractive multivalued map is introduced. Then, various fixed point theorems are established for such objects with (strong or weak) inwardness properties.

MSC:
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Alber, Ya.I.; Guerre-Delabriere, S., Principles of weakly contractive maps in Hilbert spaces, (), 7-22 · Zbl 0897.47044
[2] Bae, J.S.; Cho, E.W.; Yeom, S.H., A generalization of the caristi – kirk fixed point theorem and its application to mapping theorems, J. Korean math. soc., 31, 29-48, (1994) · Zbl 0842.47035
[3] Bae, J.S.; Park, S., Remark on the caristi – kirk fixed point theorem, Bull. Korean math. soc., 19, 57-60, (1983) · Zbl 0519.54032
[4] Boyd, D.W.; Wong, J.S.W., On nonlinear contractions, Proc. amer. math. soc., 20, 458-464, (1969) · Zbl 0175.44903
[5] Brezis, H.; Browder, F.E., A general principle on ordered sets in nonlinear functional analysis, Adv. math., 21, 355-364, (1976) · Zbl 0339.47030
[6] Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions, Trans. amer. math. soc., 215, 241-251, (1976) · Zbl 0305.47029
[7] Deimling, K., Multivalued differential equations, (1992), de Gruyter Berlin · Zbl 0760.34002
[8] Guo, C.L., Fixed point theorems for singlevalued mappings and multivalued mappings on complete metric spaces, Chinese J. math., 19, 31-53, (1991) · Zbl 0768.54032
[9] Lim, T.C., A fixed point theorem for weakly inward multivalued contractions, J. math. anal. appl., 247, 323-327, (2000) · Zbl 0957.47040
[10] Martinez-Yanez, C., A remark on weakly inward contractions, Nonlinear anal., 16, 847-848, (1991) · Zbl 0735.47032
[11] Mizoguchi, N.; Takahashi, W., Fixed point theorems for multivalued mappings on complete metric spaces, J. math. anal. appl., 141, 177-188, (1989) · Zbl 0688.54028
[12] Reich, S., Some fixed point problems, Atti. accad. naz. lincei, 57, 194-198, (1974) · Zbl 0329.47019
[13] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear anal., 47, 2683-2693, (2001) · Zbl 1042.47521
[14] Yi, H.W.; Zhao, Y.C., Fixed point theorems for weakly inward multivalued mappings and their randomizations, J. math. anal. appl., 183, 613-619, (1994) · Zbl 0815.47072
[15] Xu, H.K., Multivalued nonexpansive mappings in Banach spaces, Nonlinear anal., 43, 693-706, (2001) · Zbl 0988.47034
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