Ciric-Reich-Rus型映射的四点类比及其非唯一不动点
Four point analogue of Ciric-Reich-Rus type mappings with non-unique fixed points
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中文总结 AI 辅助
本文提出广义四边形Ciric-Reich-Rus型映射作为四点类比，在完备及非完备度量空间中建立其非唯一不动点定理，并证明映射在不动点处连续，通过渐近正则性扩展适用性。
中文摘要 AI 辅助
本文引入并研究了一类新的映射，称为广义四边形Ciric-Reich-Rus型映射，它是Ciric-Reich-Rus型映射的四点类比。我们在完备度量空间中，在映射没有素数周期2和3的周期点的条件下，建立了这些映射不动点的存在性和非唯一性，且最多可能存在三个不动点。我们确定，虽然这些映射在其定义域内通常是不连续的，但它们在不动点处必须是连续的。通过施加额外的约束，特别是渐近正则性和连续性，我们将不动点定理的适用性扩展到更广泛的映射类。最后，我们在不一定完备的度量空间中，获得了广义四边形Ciric-Reich-Rus型映射的不动点定理。文中提供了几个说明性例子来验证理论结果，并证明我们的新类与现有概念的独立性。
英文摘要
In this paper, we introduce and study a new class of mappings termed generalized quadrilateral Ciric-Reich-Rus type mappings, which serve as a four-point analogue of Ciric- Reich-Rus type mappings. We establish the existence and non-uniqueness of fixed points, with at most three fixed points possible for these mappings in complete metric spaces under the condition that the mapping has no periodic points of prime period 2 and 3. We determine that while these mappings are often discontinuous within their domain of definition, they must be continuous at their fixed points. By applying additional constraints, notably asymptotic regularity and continuity, we broaden the applicability of fixed-point theorems to include a broader class of mappings. At the end, we attain fixed point theorems for generalized quadrilateral Ciric- Reich-Rus type mappings in metric spaces that are not necessarily complete. Several illustrative examples are provided to validate the theoretical results and demonstrate the independence of our new class from existing notions.
