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Metric fixed point results for generalized contractive mappings and applications. (English) Zbl 07289978
Summary: In this paper, we establish some new results on the existence of fixed points for general multivalued contractive mappings with respect to \(\omega\)-distance. In support of our results, example and applications are also presented. Our results either improve or generalize results of metric fixed point theory, including the corresponding fixed point results of S. B. Nadler jun. [Pac. J. Math. 30, 475–488 (1969; Zbl 0187.45002)], N. Mizoguchi and W. Takahashi [J. Math. Anal. Appl. 141, No. 1, 177–188 (1989; Zbl 0688.54028)], T. Suzuki and W. Takahashi [Topol. Methods Nonlinear Anal. 8, No. 2, 371–382 (1996; Zbl 0902.47050)], the first author [JP J. Fixed Point Theory Appl. 2, No. 2, 169–175 (2007; Zbl 1152.54360)] and many others.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54H25 Fixed-point and coincidence theorems (topological aspects)
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