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Full Description
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.
Contents
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.
