Fixed point theorems in graphical cone metric spaces and application to a system of initial value problems
Satish Shukla, Nikita Dubey, Rahul Shukla
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.
Topics & Concepts
MathematicsMetric spaceCone (formal languages)Metric (unit)Product metricConvex metric spaceFixed-point theoremFixed pointPure mathematicsBanach spaceDiscrete mathematicsMetric mapInjective metric spacePoint (geometry)Algebra over a fieldMathematical analysisAlgorithmGeometryEconomicsOperations managementFixed Point Theorems AnalysisAdvanced Differential Geometry Research