Approximate Fixed Points of Nonexpansive Mappings
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Beschreibung
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.
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.
Halpern-type iterations and of iterations of alternative iterative methods are studied for various classes Illustrates solving fixed point problems and common fixed point problems for various classes of nonlinear mappings Contains solutions to difficult problems which are considered at the first time in the literature
Autor*in
Alexander J. Zaslavski
Themen in »Approximate Fixed Points of Nonexpansive Mappings«
nonexpansive mappings approximate fixed point Halpern interations Krasnoselskii-Mann interations asymptotic regularity set-valued mapping alternative iterative methods fixed point problem Perov contraction mapping cyclical mapping monotone mappings