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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.

Iterative methods (Mathematics) --- Fixed point theory --- Hilbert space --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Applied Mathematics --- Operations Research --- Calculus --- Fixed point theory. --- Hilbert space. --- Mathematics. --- Functional analysis. --- Operator theory. --- Numerical analysis. --- Mathematical optimization. --- Calculus of variations. --- Optimization. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Operator Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Banach spaces --- Hyperspace --- Inner product spaces --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Iteration (Mathematics) --- Numerical analysis