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Set-valued fixed-point theorems for generalized contractive mappings without the Hausdorff metric. (English) Zbl 1229.54050
Summary: In this paper, the concept of a set-valued contractive mapping is considered by using the idea of a generalized distance, such as the $\tau$-distance, in metric spaces without using the concept of the Hausdorff metric. Furthermore, under some mild conditions, we provide the existence theorems for fixed-point problems of the considered mapping. Hence, our results can be viewed as a generalization and improvement of many recent results.

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces
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##### References:
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