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arXiv · 2603.10556

$F$-Contraction with an Auxiliary Function and Its Application to Terrain-Following Airplane Navigation

Irom Shashikanta Singh·Yumnam Mahendra Singh
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Abstract

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.

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Irom Shashikanta Singh, Yumnam Mahendra Singh. 2026-03-11. $F$-Contraction with an Auxiliary Function and Its Application to Terrain-Following Airplane Navigation. https://arxiv.org/abs/2603.10556

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