We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.

中文翻译：

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关于p循环求和收缩的最佳邻近点

我们提出了一个条件，可以保证对于一类广泛的循环图（称为p循环求和图），在完整度量空间（或一致凸Banach空间）中存在固定（或最佳邻近）点并具有唯一性。这些结果概括了定点理论的一些已知结果。如果基础空间的凸模量是幂类型的，我们将为与所研究的地图类相关的Picard迭代找到固定（或最佳邻近）点的先验和后验误差估计。我们通过一些应用程序和示例来说明结果。