Fixed point theorems of contractive mappings in cone b -metric spaces and applications

Fixexd point theory and applications

Shaoyuan Xu¹  Huaping Huang² 

[1] School of Mathematics and Computer, Gannan Normal University, Ganzhou, China;School of Mathematics and Statistics, Hubei Normal University, Huangshi, China

关键词: cone b-metric space;    fixed point;    periodic boundary problem;   

DOI  :  10.1186/1687-1812-2013-112

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we present some new examples in cone b-metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces. The results not only directly improve and generalize some fixed point results in metric spaces and b-metric spaces, but also expand and complement some previous results in cone metric spaces. In addition, we use our results to obtain the existence and uniqueness of a solution for an ordinary differential equation with a periodic boundary condition.

【 授权许可】

CC BY