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The book contains fourteen chapters. It devote to study the iteration methods for nonlinear operators and semigroups, equilibrium problems, multiple-set split feasibility problems, global vector solutions to a Parametric Generalized System. The primary aim of this book is intended to be useful to graduate students and mathematicians, both pure and applied, who need a simple and direct presentation of the fundamentals of the theory algorithm and applications of nonlinear analysis, convex analysis and optimization theory.