Feng, Yuqiang; Liu, Sanyang Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings. (English) Zbl 1094.47049 J. Math. Anal. Appl. 317, No. 1, 103-112 (2006). In this paper, the famous Banach contraction principle and Caristi’s fixed point theorem are generalized to the case of multi-valued mappings. The results are extensions of Nadler’s fixed point theorem and some Caristi type theorems for multi-valued operators. Reviewer: Zhang Xian (Xiamen) Cited in 24 ReviewsCited in 159 Documents MSC: 47H10 Fixed-point theorems 47H04 Set-valued operators 54H25 Fixed-point and coincidence theorems (topological aspects) 54C60 Set-valued maps in general topology Keywords:complete metric space; Banach contraction principle; Caristi’s fixed point theorem; Nadler’s fixed point theorem; multivalued mappings Citations:Zbl 0187.45002; Zbl 0688.54028; Zbl 0930.91001; Zbl 0738.49009 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 30, 475-487 (1969) · Zbl 0187.45002 [2] Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc., 215, 241-251 (1976) · Zbl 0305.47029 [3] Jachymski, J. R., Caristi’s fixed point theorem and selections of set-valued contractions, J. Math. Anal. Appl., 227, 55-67 (1998) · Zbl 0916.47044 [4] Zhong, C. K.; Zhu, J.; Zhao, P. H., An extension of multi-valued contraction mappings and fixed points, Proc. Amer. Math. Soc., 128, 2439-2444 (2000) · Zbl 0948.47058 [5] Branciari, A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29, 531-536 (2002) · Zbl 0993.54040 [6] Naidu, S. V.R., Fixed-point theorems for a broad class of multimaps, Nonlinear Anal., 52, 961-969 (2003) · Zbl 1029.54049 [7] Kirk, W. A., Caristi’s fixed-point theorem and metric convexity, Colloq. Math., 36, 81-86 (1976) · Zbl 0353.53041 [8] 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 [9] Aubin, J. P., Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math. (1998), Springer-Verlag: Springer-Verlag Berlin · Zbl 0930.91001 [10] Wang, T., Fixed point theorems and fixed point stability for multivalued mappings on metric spaces, J. Nanjing Univ. Math. Baq., 6, 16-23 (1989) · Zbl 0715.54034 [11] Aubin, J. P.; Siegel, J., Fixed point and stationary points of dissipative multi-valued maps, Proc. Amer. Math. Soc., 78, 391-398 (1980) · Zbl 0446.47049 [12] Covitz, H.; Nadler, S. B., Multi-valued contraction mappings in generalized metric space, Israel J. Math., 8, 5-11 (1970) · Zbl 0192.59802 [13] Zhang, S. S.; Luo, Q., Set-valued Caristi fixed point theorem and Ekeland’s variational principle, Appl. Math. Mech.. Appl. Math. Mech., Appl. Math. Mech. (English Ed.), 10, 2, 119-121 (1989), (in Chinese), English translation: · Zbl 0738.49009 [14] Petruşel, A.; Sîntămărian, A., Single-valued and multi-valued Caristi type operators, Publ. Math. Debrecen, 60, 167-177 (2002) · Zbl 1003.47041 [15] Van Hot, L., Fixed point theorems for multi-valued mapping, Comment. Math. Univ. Carolin., 23, 137-145 (1982) · Zbl 0492.47035 [16] Agarawl, R. P.; O’Regan, D. O.; Shahzad, N., Fixed point theorem for generalized contractive maps of Meir-Keeler type, Math. Nachr., 276, 3-22 (2004) · Zbl 1086.47016 [17] Jachymski, J. R., Converses to fixed point theorems of Zeremlo and Caristi, Nonlinear Anal., 52, 1455-1463 (2003) · Zbl 1030.54033 [18] Vijayaraju, P.; Rhoades, B. E.; Mohanraj, R., A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 15, 2359-2364 (2005) · Zbl 1113.54027 [19] Feng, Y.; Liu, S., Fixed point theorems for multi-valued operators in partial ordered spaces, Soochow J. Math., 30, 461-469 (2004) · Zbl 1084.47046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.