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New existence results and generalizations for coincidence points and fixed points without global completeness. (English) Zbl 1267.54042
Author’s abstract: Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde’s fixed point theorem [M. Berinde and V. Berinde, J. Math. Anal. Appl. 326, No. 2, 772–782 (2007; Zbl 1117.47039)], Mizoguchi-Takahashi’s fixed point theorem [N. Mizoguchi and W. Takahashi, J. Math. Anal. Appl. 141, No. 1, 177–188 (1989; Zbl 0688.54028)], Kikkawa-Suzuki’s fixed point theorem [M. Kikkawa and T. Suzuki, Nonlinear Anal., Theory Methods Appl. 69, No. 9, A, 2942–2949 (2008; Zbl 1152.54358)], and some other well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are presented.
54H25Fixed-point and coincidence theorems in topological spaces
54C60Set-valued maps (general topology)
54E35Metric spaces, metrizability