具有Banach代数的锥b-度量空间上广义g-拟压缩映射的不动点定理及其应用  

Fixed Point Theorems for Generalized g-Quasi-Contractions in Cone b-Metric Spaces over Banach Algebras and Applications

作　　者：许绍元 程素玉 

机构地区：[1]韩山师范学院数学与统计学院,广东潮州521041 [2]韩山师范学院图书馆,广东潮州521041

出　　处：《应用数学》2017年第4期897-907,共11页Mathematica Applicata

基　　金：韩山师范学院2016年度创新强校工程项目"非线性分析及其应用研究学科团队"(Z16084)

摘　　要：本文在具有Banach代数的锥b-度量空间上引入广义g-拟压缩映射,无需正规性条件,得到了广义g-拟压缩映射的不动点存在唯一性,从而将′Ciri′c不动点定理推广到具有Banach代数的锥b-度量空间的情形,主要结果改进和推广了有关文献中的相应结论,并将有关结果应用于非线性积分方程.In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorem for the generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. The main results generalize, extend the corresponding results in the literature. As a result, we extend the famous Cirid fixed point theorem to the version in the setting of cone b-metric spaces over Banach algebras. In addition, we apply our main results to some nonlinear integral equations.

关 键 词：具有Banach代数的锥b-度量空间 非正规锥 广义g-拟压缩映射 不动点定理 非线性积分方程 

分 类 号：O177.91[理学—数学]