O-度量空间上广义压缩映射的不动点
Fixed points of generalized contractions on O-metric spaces
AI总结：
本文在推广了多种度量类型的O-度量空间框架下，利用作为三角不等式自然推广的多边形O-不等式，建立了压缩与广义压缩映射的不动点定理。
摘要：
O-度量空间类推广了文献中包括度量空间、b-度量空间和超度量空间在内的若干现有度量类型。本文讨论了由O-度量诱导的拓扑性质，并在该框架下建立了压缩映射与广义压缩映射的不动点定理。这些定理的证明大量依赖于多边形O-不等式，它是三角不等式的自然推广，其构造引出了遵循函数模式的O-级数概念。
英文摘要：
The class of O-metric spaces generalize several existing metric-types in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and establish in the setting, fixed point theorems of contractions and generalized contractions. The proofs of the theorems rely heavily on polygon O-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the notion of O-series following a pattern of functions.
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。
