On Generalized Nonexpansive Maps in Banach Spaces
Kifayat Ullah, Junaid Ahmad, Manuel De la Sen
Abstract
We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized α -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.
Topics & Concepts
ExpansiveClass (philosophy)MathematicsBanach spaceRegular polygonContext (archaeology)Pure mathematicsConvergence (economics)Computer scienceGeometryArtificial intelligenceGeographyMaterials scienceArchaeologyEconomicsComposite materialEconomic growthCompressive strengthOptimization and Variational AnalysisFixed Point Theorems AnalysisAdvanced Optimization Algorithms Research