This book, "Iterative Approximation of Fixed Points" by Vasile Berinde, is a comprehensive survey of the most significant contributions to the approximation of fixed points of nonlinear contractive mappings. The book is divided into several chapters, each focusing on different iterative methods such as the Picard iteration, Krasnoselskij iteration, Mann iteration, and Ishikawa iteration. Each chapter includes detailed proofs, exercises, and bibliographical comments to provide a thorough understanding of the subject.
The second edition of the book has been revised and enlarged, incorporating updated references and new sections to enhance the coverage of the topic. The author emphasizes the importance of constructive fixed point theorems, which not only establish the existence and uniqueness of fixed points but also provide methods for approximating these points and information on their data dependence.
Key changes in the second edition include an expanded bibliography, recent results, and new directions of investigation. The book aims to provide a balanced and up-to-date overview of the field, making it a valuable resource for postgraduate students, PhD students, and researchers in the area of fixed point theory and its applications.This book, "Iterative Approximation of Fixed Points" by Vasile Berinde, is a comprehensive survey of the most significant contributions to the approximation of fixed points of nonlinear contractive mappings. The book is divided into several chapters, each focusing on different iterative methods such as the Picard iteration, Krasnoselskij iteration, Mann iteration, and Ishikawa iteration. Each chapter includes detailed proofs, exercises, and bibliographical comments to provide a thorough understanding of the subject.
The second edition of the book has been revised and enlarged, incorporating updated references and new sections to enhance the coverage of the topic. The author emphasizes the importance of constructive fixed point theorems, which not only establish the existence and uniqueness of fixed points but also provide methods for approximating these points and information on their data dependence.
Key changes in the second edition include an expanded bibliography, recent results, and new directions of investigation. The book aims to provide a balanced and up-to-date overview of the field, making it a valuable resource for postgraduate students, PhD students, and researchers in the area of fixed point theory and its applications.