The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with different behaviors have been presented over the last decades. Convergence conditions have become one of the most studied topics in recent mathematical research. One of the most well-known conditions are the Kantorovich conditions, which has allowed many researchers to experiment with all kinds of conditions. In recent years, several authors have studied different modifications of the mentioned conditions considering inter alia, Holder conditions, alpha-conditions or even convergence in other spaces. In this monograph, the authors present the complete work within the past decade on convergence and dynamics of iterative methods. It acts as an extension of their related publications in these areas. The chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter, in order to allow the reader to refer to previous ideas. For these reasons, several advanced courses can be taught using this book. This book intends to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable for researchers, graduate students and seminars in the above subjects, and it would be an excellent addition to all science and engineering libraries.

Table of Contents:
Preface; Convergence of Halley's Method Under Centered Lipschitz Condition on the Second Frechet Derivative; Semilocal Convergence of Steffensen-type Algorithms; Some Weaker Extensions of the Kantorovich Theorem for Solving Equations; Improved Convergence Analysis of Newton's Methods; Extending the Applicability of Newton's Method; Extending the Applicability of Newton's Method for Sections in Riemannian Manifolds; Two-step Newton Methods; Discretized Newton-Tikhonov Method; Relaxed Secant-type Methods; Newton-Kantorovich Method for Analytic Operators; Iterative Regularization Methods for Ill-posed Hammerstein Type Operator Equations; Local Convergence of a Fifth Order Method in Banach Space; Local Convergence of the Gauss-Newton Method; Expanding the Applicability of the Gauss-Newton Method for Convex Optimization Under a Majorant Condition; An Analysis of Lavrentiev Regularization Methods & Newton-type Iterative Methods for Nonlinear Ill-posed Hammerstein-type Equations; Local Convergence of a Multi-point-parameter Newton-like Methods in Banach Space; On an Iterative Method for Unconstrained Optimization; Inexact two-point Newton-like Methods Under General Conditions; Index.