Chatterjea不动点定理的一个至多具有两个不动点的三点推广
A three point extension of Chatterjea's fixed point theorem with at most two fixed points
AI总结：
本文提出Chatterjea型映射的三点类似物，证明其与原始映射不同，建立广义映射的不动点定理并揭示与其他映射类型的联系，且在非完备度量空间中也得到两个不动点定理。
摘要：
本文在度量空间内引入了一类新的映射，特别关注于已确立的Chatterjea型映射的三点类似物。我们证明了Chatterjea型映射与其三点类似物是不同类别的映射。建立了广义Chatterjea型映射的一个不动点定理。证明了这些映射在不动点处是连续的。发现了广义Chatterjea型映射、广义Kannan型映射、Chatterjea型映射以及收缩三角形周长的映射之间的联系。此外，我们在度量空间中推导出两个广义Chatterjea型映射的不动点定理，即使完备性并非必需。
英文摘要：
In this paper, we introduce a new category of mappings within metric spaces, specifically focusing on three-point analogs of the well-established Chatterjea type mappings. We demonstrate that Chatterjea type mappings and their three-point analogs are different classes of mappings. A fixed point theorem for generalized Chatterjea type mappings is established. It is shown that these mappings are continuous at fixed point. Connections between generalized Chatterjea type mappings, generalized Kannan type mappings, Chatterjea type mappings, and mappings contracting perimeters of triangles are found. Additionally, we derive two fixed point theorems for generalized Chatterjea type mappings in metric spaces, even when completeness is not mandatory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
