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New cone fixed point theorems for nonlinear multivalued maps with their applications. (English) Zbl 1218.54037
Summary: We first establish some new types of fixed point theorems for nonlinear multivalued maps in cone metric spaces. From those results, we obtain new fixed point theorems for nonlinear multivalued maps in metric spaces and the generalizations of Mizoguchi-Takahashi’s fixed point theorem and Berinde-Berinde’s fixed point theorem. Some applications to the study of metric fixed point theory are given.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54E99Topological spaces with richer structures
References:
[1]Chen, G. Y.; Huang, X. X.; Yang, X. Q.: Vector optimization, Lecture notes in economics and mathematical systems 541 (2005)
[2]Du, W. -S.: A note on cone metric fixed point theory and its equivalence, Nonlinear anal. 72, 2259-2261 (2010) · Zbl 1205.54040 · doi:10.1016/j.na.2009.10.026
[3]Nieto, J. J.; Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[4]Nieto, J. J.; Rodríguez-López, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta math. Sinica 23, 2205-2212 (2007) · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[5]Rezapour, Sh.; Hamlbarani, R.: Some notes on the paper ”cone metric spaces and fixed point theorems of contractive mappings”, J. math. Anal. appl. 345, 719-724 (2008) · Zbl 1145.54045 · doi:10.1016/j.jmaa.2008.04.049
[6]O’regan, D.; Petruşel, A.: Fixed point theorems for generalized contractions in ordered metric spaces, J. math. Anal. appl. 341, 1241-1252 (2008) · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
[7]O’regan, D.; Zima, M.: Leggett–Williams theorems for coincidences of multivalued operators, Nonlinear anal. 68, 2879-2888 (2008) · Zbl 1152.47041 · doi:10.1016/j.na.2007.02.034
[8]Altun, I.; Damjanović, B.; Djorić, D.: Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. math. Lett. 23, 310-316 (2010) · Zbl 1197.54052 · doi:10.1016/j.aml.2009.09.016
[9]Huang, L. -G.; Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. math. Anal. appl. 332, 1468-1476 (2007) · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
[10]Du, W. -S.: Some new results and generalizations in metric fixed point theory, Nonlinear anal. 73, 1439-1446 (2010) · Zbl 1190.54030 · doi:10.1016/j.na.2010.05.007
[11]Taylor, A. E.; Lay, D. C.: Introduction to functional analysis, (1980) · Zbl 0501.46003
[12]Aubin, J. -P.; Cellina, A.: Differential inclusions, (1994)
[13]Downing, D.; Kirk, W. A.: Fixed point theorems for set-valued mappings in metric and Banach spaces, Math. japon. 22, 99-112 (1977) · Zbl 0372.47030
[14]Berinde, M.; Berinde, V.: On a general class of multi-valued weakly Picard mappings, J. math. Anal. appl. 326, 772-782 (2007) · Zbl 1117.47039 · doi:10.1016/j.jmaa.2006.03.016
[15]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 · doi:10.1016/0022-247X(89)90214-X
[16]Jr., S. B. Nadler: Multi-valued contraction mappings, Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002