Solving nonlinear ϕ -strongly accretive operator equations by a one-step-two-mappings iterative scheme

A three-step iterative scheme for solving nonlinear φ-strongly accretive operator equations in Banach spaces

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces

We use Nadler’s theorem and the resolvent operator technique for m-accretive mappings to suggest an iterative algorithm for solving generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces. We prove the existence of solutions for our inclusions without compactness assumption and the convergence of the iterative sequences generated by the algorithm i...

Three-Step Iterative Method for Solving Nonlinear Equations

In this paper, a published algorithm is investigated that proposes a three-step iterative method for solving nonlinear equations. This method is considered to be efficient with third order of convergence and an improvement to previous methods. This paper proves that the order of convergence of the previous scheme is two, and the efficiency index is less than the corresponding Newton’s method. I...

An Iterative Scheme for Solving Nonlinear Equations with Monotone Operators

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with monotone operators is proposed and its convergence is proved. A discrepancy principle is proposed and justified. A priori and a posterior...