Abstract:

The authors obtain several theorems of the existence and uniqueness of fixed point for contractive mappings under c-distance in cone metric spaces over Banach algebras without the assumptions of normality of cones and the continuity of mappings. The results greatly improve and complement some previous results. Moreover, a supportive example to illustrate the main assertions is also given. Otherwise, by solving the problem of existence and uniqueness for an elementary equation, a significant application for the obtained results is presented.

Key words: cone metric space over Banach algebra, c-distance, continuity, normality, fixed point

摘要：

在不考虑映射的连续性和锥的正规性条件下, 得到赋值Banach代数的锥度量空间中c-距离意义下压缩型映射不动点的存在性和唯一性定理, 在很大程度上改进和补充了前人的结果, 并举例验证了得到的结论。另外, 通过解决一个初等方程解的存在性和唯一性问题, 说明了所得结果的一个重要应用。

关键词: 赋值Banach代数的锥度量空间; c-距离, 连续性, 正规性, 不动点