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We analyze the global convergence for the Krasnoselskij method. More specifically, we obtain domains of global convergence in which we locate and separate fixed points of a given operator. To do that, we use auxiliary points instead of imposing conditions on the solution, that is generally unknown. Then, we apply our study to obtain fixed point type results. We finish our study by applying the results to Fredholm integral equations. [ABSTRACT FROM AUTHOR]

From decomposition method for operators, we consider a Newton‐Steffensen iterative scheme for approximating a solution of nonlinear Fredholm integral equations with non‐differentiable Nemystkii operator. By means of a convergence study of the iterative scheme applied to this type of nonlinear Fredholm integral equations, we obtain domains of existence and uniqueness of solution for these equations. In addition, we illustrate this study with a numerical experiment. [ABSTRACT FROM AUTHOR]

In this article, we consider two parametric classes of derivative free iterative methods of high order of convergence in Banach spaces. We study local and semilocal convergence results in Banach spaces for both families of iterative processes. We carry out a numerical application to solve a nonlinear and nondifferentiable Fredholm integral equation in the Banach space of continuous functions with the maximum norm. [ABSTRACT FROM AUTHOR]

In this article, an inverse free Steffensen-type method is introduced. The method is applied to approximate the systems of equations associated to implicit schemes approximating a stiff differential equation. The method has quadratic convergence without evaluating neither any derivative nor inverse operator. Finally, hypotheses ensuring the semilocal convergence and the R-order of convergence are presented. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of two high-order families of frozen Newton-type methods. The methods are free of bilinear operators, which constitute the main limitation of the classical high-order iterative schemes. Both families are natural generalizations of an efficient third-order method. Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the semilocal convergence of k-steps Newton's method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the Fréchet derivative satisfies the Lipschitz continuity, we define appropriate recurrence relations for obtaining the domains of convergence and uniqueness. We also define the accessibility regions for this iterative process in order to guarantee the semilocal convergence and perform a complete study of their efficiency. Our final aim is to apply these theoretical results to solve a special kind of conservative systems. [ABSTRACT FROM AUTHOR]

Newton's method and Kurchatov's method are iterative processes known for their fast speed of convergence. We construct from both methods an iterative method to approximate solutions of nonlinear equations given by a nondifferentiable operator, and we study its semilocal convergence in Banach spaces. Finally, we consider several applications of this new iterative process. [ABSTRACT FROM PUBLISHER]