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Approximating fixed points of nonexpansive mappings and their generalizations by iterative algorithms have been flourishing areas of research for the past few decades. There are two approaches in this field; generalizing class of mappings and generalizing the discussion spaces. The purpose of this book in first direction is to approximate fixed points of (i) asymptotically nonexpansive mappings; (ii) multivalued nonexpansive mappings; (iii) multivalued *-nonexpansive mappings in Banach spaces. In the second direction, we approximate fixed points of nonexpansive mappings in CAT(0) metric spaces and study variational inequalities for strict pseudocontractive mappings.