Abstract In this work, we show that the existence of fixed points of F-contraction mappings in function weighted metric spaces can be ensured without third condition ( F 3 ) (F3) imposed on Wardowski function F :(0, ∞ ) → ℜ F\mathrm{:(0,\hspace{0.33em}}\infty )\to \Re . The present article investigates (common) fixed points of rational type F-contractions for single-valued mappings. The article employs Jleli and Samet’s perspective of a new generalization of a metric space, known as a function weighted metric space. The article imposes the contractive condition locally on the closed ball, as well as, globally on the whole space. The study provides two examples in support of the results. The presented theorems reveal some important corollaries. Moreover, the findings further show the usefulness of fixed point theorems in dynamic programming, which is widely used in optimization and computer programming. Thus, the present study extends and generalizes related previous results in the literature in an empirical perspective.

中文翻译：

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函数加权度量空间中 F 收缩的应用分析

摘要 在这项工作中，我们证明了在函数加权度量空间中 F 收缩映射不动点的存在可以确保，而无需对 Wardowski 函数 F 施加第三个条件 ( F 3 ) (F3) :(0, ∞ ) → ℜ F \mathrm{:(0,\hspace{0.33em}}\infty )\to \Re 。本文研究了单值映射的有理型 F 收缩的（公共）不动点。本文采用 Jleli 和 Samet 对度量空间的新概括的观点，称为函数加权度量空间。该文章将收缩条件局部施加到封闭球上，以及全局施加到整个空间上。该研究提供了两个例子来支持结果。提出的定理揭示了一些重要的推论。此外，研究结果进一步表明不动点定理在动态规划中的有用性，它广泛用于优化和计算机编程。因此，本研究从实证的角度扩展和概括了文献中的相关先前结果。