Approximate Fixed Points of Nonexpansive Mappings

2024
ISBN: 978-3-031-70709-4
Verlag: Springer Nature Switzerland

Buch, Englisch, Band 80, 526 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 969 g

Reihe: Developments in Mathematics

Fixed point theory of nonlinear operators has been a rapidly growing area of research and plays an important role in the study of variational inequalities, monotone operators, feasibility problems, and optimization theory, to name just several. This book discusses iteration processes associated with a given nonlinear mapping which generate its approximate fixed point and in some cases converge to a fixed point of the mapping. Various classes of nonlinear single-valued and set-valued mappings are considered along with iteration processes under the presence of computational errors. Of particular interest to mathematicians working in fixed point theory and nonlinear analysis, the added value for the reader are the solutions presented to a number of difficult problems in the fixed point theory which have important applications.

Zielgruppe

Research

Autoren/Hrsg.

Zaslavski, Alexander J.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Preface.- 1. Introduction.- 2. Asymptotic regularity for iterations of nonexpansive mappings.- 3. Asymptotic regularity for iterations of monotone nonexpansive mappings.- 4. Asymptotic regularity of uniformly locally nonexpansive mappings.- 5. Asymptotic regularity property in spaces with graphs.- 6. Inexact Viscosity Approximation Methods in Hilbert Spaces.- 7. A common fixed point problem.- 8. Perov contraction mappings.- 9. Cyclical mappings.- 10. Monotone nonexpansive mappings.- 11. Uniformly Locally Contractive Mappings.- 12. Set-valued mappings.- 13. Nonexpansive mappings in spaces with graphs.- References.- Index.

Über Autor(innen)

Alexander J. Zaslavski  is a senior researcher at the Technion - Israel Institute of Technology. He was born in Ukraine in 1957 and got his PhD in Mathematical Analysis in 1983,  The Institute of Mathematics, Novosibirsk. He is the author of 26 research monographs and more than 600 research papers and editor of more than 70 edited volumes and journal  special issues. He is the Founding Editor and Editor-in Chief of the journal , and Editor-in-Chief of  the journal .  His area of research contains nonlinear functional analysis, control theory, optimization, calculus of variations, dynamical systems theory, game theory and mathematical economics.