On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

On q-Newton-Kantorovich method for solving systems of equations

Starting from q-Taylor formula for the functions of several variables and mean value theorems in q-calculus which we prove by ourselves, we develop a new methods for solving the systems of equations. We will prove its convergence and we will give an estimation of the error. 2004 Elsevier Inc. All rights reserved.

Newton - Secant method for solving operator equations ∗

where F is a Fréchet-differentiable operator defined on an open subset D of a Banach space X with values in a Banach space Y . Finding roots of Eq.(1) is a classical problem arising in many areas of applied mathematics and engineering. In this study we are concerned with the problem of approximating a locally unique solution α of Eq.(1). Some of the well known methods for this purpose are the f...

Solving nonlinear integral equations in the Urysohn form by Newton-Kantorovich-quadrature method

On generalized Newton method for solving operator inclusions

In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ∋ 0, where F is a Fréchet differentiable operator, G is a maximal monotone operator and T is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and...

On Newton-Like Method for Solving Generalized Nonlinear Operator Equations in Banach Spaces

The purpose of this paper is to prove existence and uniqueness theorem for solving an operator equation of the form F(x)+ G(x) = 0, where F is a Gâteaux differentiable operator and G is a Lipschitzian operator defined on an open convex subset of a Banach space. Our result extends and improves the previously known results in recent literature. 2010 Mathematics Subject Classification: 49M15, 65K10