AI 中文总结
本研究针对O-度量这一新型广义度量结构，构建了统一解析框架，通过引入广义ω-级数建立分离原理，得到压缩参数区间与收敛准则，还推导了O-度量及b-度量空间的不动点定理。
AI 中文摘要
O-度量的概念是近期提出的，它通过将标准三角不等式的加法运算替换为可能不满足结合律的二元运算，对多种度量型结构进行了推广。这种非结合性自然延伸到广义多边形不等式和模式化复合中。本研究针对此类场景中出现的不等式构建了解析框架，通过引入由容许控制函数φ控制的广义ω-级数，建立了一个分离原理，可解决形如u ≤ v ω φ(k,u)的不等式。该结果为模式化复合提供了收敛准则，并确定了容许收缩参数k的区间。作为应用，得到了O-度量空间上映射的若干Ćirić型不动点定理，以及对应b-度量空间的相关结果。该方法为研究广义度量空间中的压缩条件和迭代过程提供了统一的解析框架。
英文摘要
The concept of O-metrics was recently introduced as a generalization of several metric-type structures by replacing the addition operation of the standard triangle inequality with a binary operation that may fail to be associative. This non-associativity naturally to generalized polygon inequalities and patterned compositions. In this work we develop an analytic framework for inequalities arising in such settings. By introducing generalized $\om$-series governed by admissible control functions $φ$, we establish a separation principle that resolves inequalities of the form $u \leq v \, \om \, φ(k,u)$. This result provides convergence criteria for patterned compositions and determines intervals for the admissible contraction parameter $k$. As application, some fixed point theorems of Ćirić type are obtained for mappings on O-metric spaces, as well as corresponding results for b-metric spaces. The approach provides a unified analytic framework for studying contractive conditions and iterative processes in generalized metric spaces.
