Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications
Ioannis K. Argyros
Abstract
A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are weaker than earlier ones without additional hypotheses? The answer is yes. In particular, we provide only one sufficient convergence criterion suitable for single-step methods. Moreover, we also give a finer convergence analysis. Numerical experiments involving boundary value problems and Hammerstein-like integral equations complete this paper.
Topics & Concepts
Banach spaceConvergence (economics)MathematicsIterative methodApplied mathematicsModes of convergence (annotated index)Operator (biology)Unconditional convergenceBoundary value problemCompact convergenceConvergence testsSpace (punctuation)Mathematical optimizationComputer scienceMathematical analysisRate of convergenceDiscrete mathematicsKey (lock)EconomicsComputer securityIsolated pointRepressorTranscription factorTopological spaceEconomic growthOperating systemChemistryTopological vector spaceBiochemistryGeneIterative Methods for Nonlinear EquationsMatrix Theory and AlgorithmsNumerical methods in inverse problems