Explicit iterative methods have been used extensively to generate a sequence approximating a solution of an equation on a Banach space setting. However, little attention has been given to the study of implicit iterative methods. We show a semi-local convergence analysis for a some general implicit and explicit iterative techniques. Illustrative applications are presented including Banach space valued functions of fractional calculus, such that all integrals are of Bochner-type.
Digital Object Identifier (DOI)
A. Anastassiou, George and K. Argyros, Ioannis
"Iterative Methods and their Applications to Banach Space Valued Functions in Abstract Fractional Calculus,"
Progress in Fractional Differentiation & Applications: Vol. 4
, Article 5.
Available at: https://dc.naturalspublishing.com/pfda/vol4/iss1/5