Iterative Solution of Nonlinear Equations with Strongly Accretive Operators

Stable Iteration Schemes for Local Strongly Pseudocontractions and Nonlinear Equations Involving Local Strongly Accretive Operators

Let T be a local strongly pseudocontractive and uniformly continuous operator from an arbitrary Banach space X into itself. Under certain conditions, we establish that the Noor iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T -stable. The related results deal with the convergence and almost stability of the Noor iteration scheme with errors of so...

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.

Regularization of Nonlinear Ill-posed Equations with Accretive Operators

We study the regularization methods for solving equations with arbitrary accretive operators. We establish the strong convergence of these methods and their stability with respect to perturbations of operators and constraint sets in Banach spaces. Our research is motivated by the fact that the fixed point problems with nonexpansive mappings are namely reduced to such equations. Other important ...

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

Iterative solution of linear equations with unbounded operators

A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space, including equations with unbounded, closed, densely defined linear operators. The method is proved to be stable towards small perturbation of the data. Some abstract results are established and used in an analysis of variational regularization method for equations with unbounded linear ope...