论文标题
在贝林德的论文中，“关于公制空间中某些固定点定理的评论”
On Berinde's paper "Comments on some fixed point theorems in metric spaces"
论文作者
论文摘要
在论文的定理1中[V. Pata，公制空间中的固定点定理，J。固定点理论应用，10（2011），299-305]，如果在间隔[0,1]中为所有参数验证了所有参数，则PICARD的函数的迭代会收敛到固定点。在最近的论文[V. Berinde，对公制空间中的某些固定点定理的评论，创建。数学。通知。 27（2018），15-20]，作者声称，Pata的结果至少在两个极端情况下没有（c）中的参数。在本说明中，我们指出，Berinde的定理1.1与PATA定理1具有视觉相似性，而定理1.1的结论仅通过恒定函数来验证。
In Theorem 1 of the paper [V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), 299-305] it is proved that Picard's iterates for a function converge to a fixed point if a certain condition (C) is verified for all parameters in the interval [0,1]. In the recent paper [V. Berinde, Comments on some fixed point theorems in metric spaces, Creat. Math. Inform. 27 (2018), 15-20], the author claims that Pata's result does not hold at least in the two extremal cases for the parameter involved in (C). In this note we point out that Berinde's Theorem 1.1 has only a visual similarity with Pata's Theorem 1, and the conclusion of Theorem 1.1 is verified only by constant functions.
