具有非唯一不动点的Ćirić-Reich-Rus型映射的三点类比
Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points
AI总结：
本文提出广义Ćirić-Reich-Rus型映射的三点类比，证明其不动点存在且非唯一，并在未必完备的度量空间中借助渐近正则性与连续性得到两个不动点定理。
摘要：
本文引入Ćirić-Reich-Rus型映射的三点类比，称为广义Ćirić-Reich-Rus型映射。我们证明这些映射在其定义域内通常表现出不连续性，但在其不动点处必须连续。我们展示了这些广义Ćirić-Reich-Rus型映射不动点的存在性与非唯一性。通过施加额外条件，特别是渐近正则性和连续性，我们将不动点定理的适用范围扩展到更广泛的映射类。最后，我们在未必完备的度量空间中得到了两个关于广义Ćirić-Reich-Rus型映射的不动点定理。
英文摘要：
In this paper, we introduce a three-point analogue of Ćirić-Reich-Rus type mappings, termed as generalized Ćirić-Reich-Rus type mappings. We demonstrate that these mappings generally exhibit discontinuity within their domain of definition but necessitate continuity at their fixed points. We showcase the existence and non-uniqueness of fixed points for these generalized Ćirić-Reich-Rus type mappings. By imposing additional conditions, specifically asymptotic regularity and continuity, we extend the applicability of fixed-point theorems to a broader class of mappings. Finally, we obtain two fixed point theorems for generalized Ćirić-Reich-Rus type mappings in metric spaces that are not necessarily complete.
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