On an iterative algorithm of Ulm-type for solving equations

Abstract

We provide a semilocal convergence analysis of an iterative algorithm for solving nonlinear operator equations in a Banach space setting. This algorithm is of order \(1.839\ldots\), and has already been studied in [3, 8, 18, 20]. Using our new idea of recurrent functions we show that a finer analysis is possible with sufficient convergence conditions that can be weaker than before, and under the same computational cost. Numerical examples are also provided in this study.

Keywords

• Banach space
• iterative algorithm
• semilocal convergence
• divided difference of operator
• Fréchet-derivative