斜边压缩映射的不动点存在性与稳定性研究及其在抛物型偏微分方程中的应用
Study of Existence and Stability of Fixed Points of Hypotenuse Contracting Mappings with Applications to Parabolic PDE
- Dr. B.C. Roy Engineering College（B.C.罗伊工程学院）
- National Institute of Technology Durgapur（杜尔加布尔国家技术学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在度量空间中引入斜边压缩映射，建立其不动点存在性与唯一性及Ulam-Hyers稳定性的充分条件，经几何分析区分其与其他压缩映射，最终将结果应用于非齐次线性抛物型PDE解的存在性证明。
AI中文摘要：
本文在度量空间框架下引入一类新的映射，其特征为能压缩直角三角形的斜边。我们建立了确保不动点存在性与唯一性的充分条件，结合几何分析与示例（含图示），将这类映射与常见的周长压缩、面积压缩等压缩映射类型区分开来。此外，我们研究了相关不动点方程的Ulam-Hyers稳定性，从而增强了该理论框架的鲁棒性。最后，将所得结果应用于证明一类非齐次线性抛物型偏微分方程（PDE）解的存在性。
英文摘要：
In this article, we introduce a novel class of mappings identified by their property of contracting the hypotenuse of a right-angled triangle in the setting of metric spaces. We establish sufficient conditions ensuring both the existence and uniqueness of fixed points. A geometric analysis, complemented by illustrative diagrams, is provided to differentiate these mappings from other familiar contraction types, namely perimeter and area contractions, supported by examples. Furthermore, we investigate the Ulam-Hyers stability of the associated fixed point equation, thereby strengthening the robustness of the theoretical framework. Finally, the derived results are applied to demonstrate the existence of solutions for a nonhomogeneous linear parabolic partial differential equation (PDE).
