$F$-Contraction with an Auxiliary Function and Its Application to Terrain-Following Airplane Navigation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911505761435648 |
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| author | Singh, Irom Shashikanta Singh, Yumnam Mahendra |
| author_facet | Singh, Irom Shashikanta Singh, Yumnam Mahendra |
| contents | This paper aims to integrate the concepts of $F$-contraction and $S^B$-contraction within the context of super metric spaces. Specifically, we introduce the concepts of $S^F$-contraction and Bianchini $S^F$-contraction. We demonstrate that these new concepts are genuine generalizations of $S^B$- and $S^K$-contractions by providing nontrivial examples. Furthermore, we establish the existence and uniqueness of fixed points for mappings that satisfy these contractions. Lastly, we apply our findings to a model describing an airplane capable of automatically following a terrain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10556 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $F$-Contraction with an Auxiliary Function and Its Application to Terrain-Following Airplane Navigation Singh, Irom Shashikanta Singh, Yumnam Mahendra General Topology Primary 47H10, Secondary 54H25 This paper aims to integrate the concepts of $F$-contraction and $S^B$-contraction within the context of super metric spaces. Specifically, we introduce the concepts of $S^F$-contraction and Bianchini $S^F$-contraction. We demonstrate that these new concepts are genuine generalizations of $S^B$- and $S^K$-contractions by providing nontrivial examples. Furthermore, we establish the existence and uniqueness of fixed points for mappings that satisfy these contractions. Lastly, we apply our findings to a model describing an airplane capable of automatically following a terrain. |
| title | $F$-Contraction with an Auxiliary Function and Its Application to Terrain-Following Airplane Navigation |
| topic | General Topology Primary 47H10, Secondary 54H25 |
| url | https://arxiv.org/abs/2603.10556 |