关于带三角函数的半度量空间中若干不动点定理的推广
On generalizations of some fixed point theorems in semimetric spaces with triangle functions
AI总结：
本文在带三角函数的半度量空间框架下推广多类经典不动点定理，并导出多类空间的推论，可用于优化、建模与算法设计。
摘要：
本文证明了 Banach、Kannan、Chatterjea、Ćirić-Reich-Rus 不动点定理，以及关于压缩三角形周长映射的不动点定理的推广。我们在由 M. Bessenyei 和 Z. Páles 引入的带三角函数的半度量空间中考虑相应映射。这种方法使我们能够推导出各类半度量空间的推论，包括度量空间、超度量空间、b-度量空间等。这些推广定理的重要性跨越优化学、数学建模和计算机科学等多个学科。它们可用于建立稳定性条件、证明最优解的存在性以及改进算法设计。
英文摘要：
In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, Ćirić-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by M. Bessenyei and Z. Páles. Such an approach allows us to derive corollaries for various types of semimetric spaces including metric spaces, ultrametric spaces, b-metric spaces etc. The significance of these generalized theorems extends across multiple disciplines, including optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design.
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。
