Iterative Methods for Fixed Point Problems in Hilbert Spaces

  • Andrzej Cegielski

Part of the Lecture Notes in Mathematics book series (LNM, volume 2057)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Andrzej Cegielski
    Pages 1-38
  3. Andrzej Cegielski
    Pages 39-103
  4. Andrzej Cegielski
    Pages 105-127
  5. Andrzej Cegielski
    Pages 129-202
  6. Andrzej Cegielski
    Pages 203-274
  7. Back Matter
    Pages 275-298

About this book

Introduction

Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

Keywords

47-02, 49-02, 65-02, 90-02, 47H09, 47J25, 37C25, 65F10 fixed point projection methods quasi-nonexpansive operator

Authors and affiliations

  • Andrzej Cegielski
    • 1
  1. 1.Faculty of Mathematics, Computer Science and EconometricsUniversity of Zielona GóraZielona GóraPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-30901-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-30900-7
  • Online ISBN 978-3-642-30901-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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