Extended domain for fifth convergence order solver

Abstract

We provide a local as well as a semi-local analysis of a fifth convergence order solver involving operators valued on Banach space for solving nonlin-ear equations. The convergence domain is extended resulting a finer convergence analysis for both types. This is achieved by locating a smaller domain included in the older domain leading this way to tighter Lips-chitz type functions. These extensions are obtained without additional hypotheses. Numerical examples are used to test the convergence crite-ria and also to show the superiority for our results over earlier ones. Our idea can be utilized to extend other solvers using inverses in a similar way.