Inertial Accelerated Algorithm for Fixed Point of Asymptotically Nonexpansive Mapping in Real Uniformly Convex Banach Spaces
M. H. Harbau, Godwin Chidi Ugwunnadi, Lateef Olakunle Jolaoso, Ahmad Abdulwahab
Abstract
In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.
Topics & Concepts
Banach spaceFixed pointRegular polygonInertial frame of referenceMathematicsConvergence (economics)Uniformly convex spaceSet (abstract data type)Weak convergenceAlgorithmPure mathematicsApplied mathematicsMathematical analysisComputer scienceGeometryBanach manifoldLp spaceComputer securityProgramming languagePhysicsAsset (computer security)EconomicsEconomic growthQuantum mechanicsOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchFixed Point Theorems Analysis