A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators

Abstract

The aim of this paper is the approximation of nonlinear equations using iterative methods. We present a unified convergence analysis for some two-point type methods. This way we compare specializations of our method using not necessarily the same convergence criteria. We consider both semilocal and local analysis. In the first one, the hypotheses are imposed on the initial guess and in the second on the solution. The results can be applied for smooth and nonsmooth operators.

Keywords

• iterative methods
• nonlinear equations
• Newton-type methods
• smooth and nonsmooth operators