C*代数值b一度量空间中的公共不动点定理

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关键词：不动点； C* 代数值b一度量空间；柯西列；相容 中图分类号：O174.1 文献标志码：A doi： 10.3969/j .issn.1673-5862.2025.05.011

Common fixed point theorems in C* -algebra valued b -metric spaces

GUAN Hongyan，LI Yunuo （College of Mathematics and Systems Science，Shenyang Normal University，Shenyang 11oo34，China）

Abstract： The Banach contraction mapping principle plays an important role in nonlinear analysis. It serves as an effective methodology for addressing the existence and uniqueness of fixed points in metric spaces and has a wide range of applications in basic mathematics，applied mathematics，and computational mathematics. In recent years，many researchers have studied the Banach contraction mapping principle from multiple perspectives，and have extended and applied it. This paper investigates the existence of common fixed points for four mappings in the context of C* -algebraic valued b -metric spaces. Firstly，a new type of contractive mappings is introduced. Secondly，a new sequence is constructed by using the inclusion relation of four mappings. Using the properties of C∗ -algebraic valued -metric spaces and contractive conditions，it is proved that the sequence is Cauchy. Finally，combining the completeness of the space and the continuity of the mappings，and the compatibility conditions，we prove that the four mappings have a unique common fixed point and a specific example is given to illustrate the validity of the results.

Key words： fixed point; C⋆ -algebra valued b -metric spaces；Cauchy sequence；compatible

不动点理论是非线性分析的重要工具，可以对许多非线性问题进行分析和求解，从而推动非线性分析理论的发展。（剩余8140字）