In this paper, the concept of strong fixed point property of a mapping is defined. The relationship between an approximating fixed point sequence and compactness is studied. The notion of a center set for a mapping is introduced. Some necessary and sufficient conditions for existence of mappings admitting a center set are presented. The results proved herein extend, generalize and improve some well-known comparable results.

中文翻译：

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赋范空间上映射的强纯定点性质

在本文中，定义了映射的强定点性质的概念。研究了近似定点序列与紧性之间的关系。介绍了映射中心集的概念。提出了允许存在中心集的映射的一些必要和充分条件。本文证明的结果扩展，推广和改进了一些众所周知的可比结果。