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On coincidence point and fixed point theorems for nonlinear multivalued maps. (English) Zbl 1231.54021
Summary: Several characterizations of ℳ𝒯-functions are first given in this paper. Applying the characterizations of ℳ𝒯-functions, we establish some existence theorems for coincidence points and fixed points in complete metric spaces. From these results, we can obtain new generalizations of Berinde-Berinde’s fixed point theorem and Mizoguchi-Takahashi’s fixed point theorem for nonlinear multivalued contractive maps. Our results generalize and improve some main results in the literature.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54C60Set-valued maps (general topology)
54E50Complete metric spaces
References:
[1]Takahashi, W.: Nonlinear functional analysis, (2000) · Zbl 0997.47002
[2]Jr., S. B. Nadler: Multi-valued contraction mappings, Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[3]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
[4]Du, W. -S.: Coupled fixed point theorems for nonlinear contractions satisfied mizoguchi-takahashi’s condition in quasiordered metric spaces, Fixed point theory and applications 2010 (2010) · Zbl 1194.54061 · doi:10.1155/2010/876372
[5]Du, W. -S.: Nonlinear contractive conditions for coupled cone fixed point theorems, Fixed point theory and applications 2010 (2010) · Zbl 1220.54022 · doi:10.1155/2010/190606
[6]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
[7]Kamran, T.: Multivalued f-weakly Picard mappings, Nonlinear anal. 67, 2289-2296 (2007) · Zbl 1128.54024 · doi:10.1016/j.na.2006.09.010
[8]Berinde, V.; Păcurar, M.: Fixed points and continuity of almost contractions, Fixed point theory 9, 23-34 (2008) · Zbl 1152.54031
[9]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
[10]Reich, S.: Some problems and results in fixed point theory, Contemp. math. 21, 179-187 (1983) · Zbl 0531.47048
[11]Daffer, P. Z.; Kaneko, H.: Fixed points of generalized contractive multi-valued mappings, J. math. Anal. appl. 192, 655-666 (1995) · Zbl 0835.54028 · doi:10.1006/jmaa.1995.1194
[12]Suzuki, T.: Mizoguchi-takahashi’s fixed point theorem is a real generalization of nadler’s, J. math. Anal. appl. 340, 752-755 (2008) · Zbl 1137.54026 · doi:10.1016/j.jmaa.2007.08.022
[13]Berinde, V.: Approximating fixed points of weak contractions using the Picard iteration, Nonlinear anal. Forum 9, 43-53 (2004) · Zbl 1078.47042
[14]W.-S. Du, S.-X Zheng, Nonlinear conditions for coincidence point and fixed point theorems, Taiwanese J. Math., in press.
[15]Suzuki, T.: Fixed point theorems for berinde mappings, Bull. kyushu inst. Tech. pure appl. Math. 58, 13-19 (2011)