Kanwal Shazia, Waheed Sana, Rahimzai Ariana Abdul, Khan Ilyas
Department of Mathematics, Government College University, Faisalabad, Pakistan.
Department of Mathematics, Education Faculty, Laghman University, Mehtarlam, Laghman, 2701, Afghanistan.
Sci Rep. 2024 Apr 2;14(1):7807. doi: 10.1038/s41598-024-58451-7.
The main goal of this study is to establish common fuzzy fixed points in the context of complete b-metric spaces for a pair of fuzzy mappings that satisfy F-contractions. To strengthen the validity of the derived results, non-trivial examples are provided to substantiate the conclusions. Moreover, prior discoveries have been drawn as logical extensions from pertinent literature. Our findings are further reinforced and integrated by the numerous implications that this technique has in the literature. Using fixed point techniques to approximate the solutions of differential and integral equations is very useful. Specifically, in order to enhance the validity of our findings, the existence result of the system of non-linear Fredholm integral equations of second-kind is incorporated as an application.
本研究的主要目标是在完备b-度量空间的背景下，为满足F-压缩的一对模糊映射建立公共模糊不动点。为了加强所得结果的有效性，提供了非平凡的例子来证实这些结论。此外，先前的发现是从相关文献中作为逻辑延伸得出的。这项技术在文献中的众多应用进一步加强并整合了我们的研究结果。使用不动点技术逼近微分方程和积分方程的解非常有用。具体而言，为了提高我们研究结果的有效性，将第二类非线性Fredholm积分方程组的存在性结果作为一个应用纳入其中。
