标题： Cq-交换映射的公共不动点通过广义Gregus型不等式 显示英文标题

标题： Common Fixed Points of Cq-Commuting Maps via Generalized Gregus-Type Inequalities

摘要： 我们建立了满足带有二次项的广义Gregus型不等式的$C_q$-交换自映射在赋范线性空间中的$q$-星形凸子集上公共不动点的存在性。 我们的框架通过以下方式扩展了经典的不动点理论： (i) 集合距离约束$\delta(\cdot, [q, \cdot])$，推广了范数条件 (ii) 通过$C_q$-交换性实现相容性，无需完全同态要求 (iii) 互反连续性替代了完整的映射连续性。 具体的例子（例如例2.6）展示了这些扩展的非平凡性。 作为应用，我们推导了最佳逼近集的不变逼近定理。 我们的结果推广了Nashine的工作\cite{Nashine2007}，并统一了若干已知的不动点定理。 显示英文摘要

摘要： We establish the existence of common fixed points for $C_q$-commuting self-mappings satisfying a generalized Gregus-type inequality with quadratic terms in $q$-starshaped subsets of normed linear spaces. Our framework extends classical fixed point theory through: (i) Set-distance constraints $\delta(\cdot, [q, \cdot])$ generalizing norm conditions (ii) Compatibility via $C_q$-commutativity without full affinity requirements (iii) Reciprocal continuity replacing full map continuity. Explicit examples (e.g., Example 2.6) demonstrate the non-triviality of these extensions. As applications, we derive invariant approximation theorems for best approximation sets. Our results generalize Nashine's work \cite{Nashine2007} and unify several known fixed point theorems.