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Fixed point theorems of multivalued monotone mappings in ordered metric spaces. (English) Zbl 1203.54052
Summary: Some new fixed point and coupled fixed point theorems for multivalued monotone mappings in ordered metric spaces are proved.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54C60Set-valued maps (general topology)
54F05Linearly, generalized, and partial ordered topological spaces
References:
[1]Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions, Trans. amer. Math. soc. 215, 241-251 (1976) · Zbl 0305.47029 · doi:10.2307/1999724
[2]Lakshmikantham, V.; Ciric, Ljubomir: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal. TMA 70, No. 2, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[3]O’regan, Donal; Petrusel, Adrian: Fixed point theorems for generalized contractions in ordered metric spaces, J. math. Anal. appl. 341, No. 2, 1241-1252 (2008) · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
[4]Ciric, Ljubomir; Cakic, Nenad; Rajovic, Miloje; Ume, Jeong Sheok: Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point theory appl., 1-11 (2008) · Zbl 1158.54019 · doi:10.1155/2008/131294
[5]Bhaskar, T. Gnana; Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal. TMA 65, No. 7, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[6]Zhang, Xian: Fixed point theorems of monotone mappings and coupled fixed point of mixed monotone mappings in ordered metric space, Acta. math. Sinica 44, No. 4, 641-646 (2001) · Zbl 1011.54038