Abstract
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.
Highlights
Fixed point theory plays a basic role in applications of many branches of mathematics
In [ ], Huang and Zhang introduced cone metric spaces as a generalization of metric spaces. They proved some fixed point theorems for contractive mappings that expanded certain results of fixed points in metric spaces
Throughout this paper, we firstly offer some new examples in cone b-metric spaces, obtain some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces
Summary
Fixed point theory plays a basic role in applications of many branches of mathematics. In [ ], Huang and Zhang introduced cone metric spaces as a generalization of metric spaces. They proved some fixed point theorems for contractive mappings that expanded certain results of fixed points in metric spaces. Throughout this paper, we firstly offer some new examples in cone b-metric spaces, obtain some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces. We always suppose that E is a Banach space, P is a cone in E with int P = ∅ and ≤ is a partial ordering with respect to P.
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