Fixed point theorems in graphical cone metric spaces and application to a system of initial value problems

Abstract

Abstract In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided.

Keywords

• Fixed point
• Graphical cone metric space
• Banach algebra
• Contraction
• System of initial value problems