Liu, Zeqing; Wu, Zhihua; Kang, Shin Min; Lee, Sunhong Some fixed point theorems for nonlinear set-valued contractive mappings. (English) Zbl 1252.54040 J. Appl. Math. 2012, Article ID 786061, 13 p. (2012). Summary: Four fixed point theorems for nonlinear set-valued contractive mappings in complete metric spaces are proved. The results presented in this paper are extensions of a few well-known fixed point theorems. Two examples are also provided to illustrate our results. Cited in 1 ReviewCited in 1 Document MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems Keywords:fixed point theorems; nonlinear set-valued contractive mappings; complete metric spaces PDF BibTeX XML Cite \textit{Z. Liu} et al., J. Appl. Math. 2012, Article ID 786061, 13 p. (2012; Zbl 1252.54040) Full Text: DOI OpenURL References: [1] L. Ćirić, “Fixed point theorems for multi-valued contractions in complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 499-507, 2008. · Zbl 1213.54063 [2] L. Ćirić, “Multi-valued nonlinear contraction mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2716-2723, 2009. · Zbl 1179.54053 [3] Y. Feng and S. Liu, “Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings,” Journal of Mathematical Analysis and Applications, vol. 317, no. 1, pp. 103-112, 2006. · Zbl 1094.47049 [4] D. Klim and D. Wardowski, “Fixed point theorems for set-valued contractions in complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 334, no. 1, pp. 132-139, 2007. · Zbl 1133.54025 [5] Z. Liu, W. Sun, S. M. Kang, and J. S. Ume, “On fixed point theorems for multivalued contractions,” Fixed Point Theory and Applications, vol. 2010, Article ID 870980, 18 pages, 2010. · Zbl 1207.54062 [6] N. Mizoguchi and W. Takahashi, “Fixed point theorems for multivalued mappings on complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 141, no. 1, pp. 177-188, 1989. · Zbl 0688.54028 [7] S. B. Nadler Jr., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475-488, 1969. · Zbl 0187.45002 [8] S. Reich, “Fixed points of contractive functions,” Bollettino dell’Unione Matematica Italiana, vol. 5, pp. 26-42, 1972. · Zbl 0249.54026 [9] S. Reich, “Some fixed point problems,” Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, vol. 57, no. 3-4, pp. 194-198, 1974. · Zbl 0329.47019 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.