We obtain a Meir–Keeler type fixed-point theorem which gives a new solution to the Rhoades’ problem on the existence of contractive mappings that admit discontinuity at the fixed point. Meir–Keeler type solutions of the Rhoades’ problem have not been reported in literature before this. Presenting a new approach, we give another solution to this problem using the set of simulation functions. To emphasize the importance of our theoretical results, we obtain two applications of the main results with some illustrative examples.

中文翻译：

---

定点间断的新结果

我们获得了一个Meir–Keeler型不动点定理，该定理为在允许不动点存在不连续性的压缩映射的存在方面为Rhoades问题提供了新的解决方案。在此之前，文献中还没有关于罗德问题的Meir–Keeler型解的报道。提出一种新方法，我们使用一组仿真函数为该问题提供了另一种解决方案。为了强调我们的理论结果的重要性，我们通过一些说明性实例获得了两种主要结果的应用。