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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| Accès en ligne: | https://arxiv.org/abs/1909.12484 |
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| _version_ | 1866910563626385408 |
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| author | Gupta, Ajit Kumar Mukherjee, Saikat |
| author_facet | Gupta, Ajit Kumar Mukherjee, Saikat |
| contents | Shimizu and Takahashi have shown that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty intersection. It is well known that the Menger convexity is a generalization of the Takahashi convexity. In this article, we acquire a nonempty intersection property, in terms of the Hausdorff metric, for Menger convex metric spaces, that also provides a class of reflexive Menger convex spaces. We introduce a generalization of $(α, β)-$generalized hybrid mapping, and using the obtained nonempty intersection property we derive the fixed point results for this generalized mapping defined on Menger convex spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_12484 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Menger Convexity and Hausdorff Metric Gupta, Ajit Kumar Mukherjee, Saikat General Topology 52A05, 47H10, 47H09 Shimizu and Takahashi have shown that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty intersection. It is well known that the Menger convexity is a generalization of the Takahashi convexity. In this article, we acquire a nonempty intersection property, in terms of the Hausdorff metric, for Menger convex metric spaces, that also provides a class of reflexive Menger convex spaces. We introduce a generalization of $(α, β)-$generalized hybrid mapping, and using the obtained nonempty intersection property we derive the fixed point results for this generalized mapping defined on Menger convex spaces. |
| title | Menger Convexity and Hausdorff Metric |
| topic | General Topology 52A05, 47H10, 47H09 |
| url | https://arxiv.org/abs/1909.12484 |