In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.

中文翻译：

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关于“一些新的不动点导致矩形度量空间与分数阶泛函微分方程的应用”的一些批评性评论

在这份手稿中，我们概括、改进和丰富了 Budhia 等人最近建立的结果。[L。Budhia，H. Aydi，AH Ansari，D. Gopal，一些新的不动点导致矩形度量空间应用于分数阶泛函微分方程，非线性分析。模型。控制, 25(4):580–597, 2020]。本文旨在为矩形度量空间中的某些结果提供更简单和更短的证明。根据我们最近的一个引理，我们表明给定的收缩条件会产生相应 Picard 序列的柯西性。获得的结果改进了文献中众所周知的可比结果。使用我们的新方法，我们证明了 Picard 序列是矩形度量空间框架中的柯西序列。我们获得的结果补充和丰富了现有 stateofart 中的几种方法。