复值b-距离空间的两类非线性压缩不动点定理
Two Nonlinear Fixed Point Theorems on Complex-Valued b-Metric Spaces
DOI: 10.12677/pm.2026.161001, PDF,    国家自然科学基金支持
作者: 杨宇轩*, 贺 飞：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 复值b-距离空间；-压缩；Geraghty压缩；不动点定理；Complex-Valued b-Metric Space； -Contractive； Geraghty Contractive； Fixed Point Theorem
摘要: 复值b-距离空间是比复值距离空间和b-距离空间更一般的空间。本文在复值b-距离空间建立ϕ-压缩不动点定理和Geraghty压缩不动点定理。这两类非线性压缩不动点定理是b-距离空间相应结果的推广，同时也为研究复值距离空间和非线性问题提供了新的工具。
Abstract: Complex-valued b-metric spaces are more general spaces than both complex-valued metric spaces and b-metric spaces. The ϕ-contractive fixed point theorems and the Geraghty contractive fixed point theorems are established in complex-valued b-metric spaces. These two types of nonlinear contraction fixed point theorems are generalizations of the corresponding results in b-metric spaces, and they also provide new tools for studying complex-valued metric spaces and nonlinear problems.
文章引用：杨宇轩, 贺飞. 复值b-距离空间的两类非线性压缩不动点定理[J]. 理论数学, 2026, 16(1): 1-11. https://doi.org/10.12677/pm.2026.161001

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