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Algorithmic Operators

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Iterative Methods for Fixed Point Problems in Hilbert Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2057))

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Abstract

In Chap. 2 we introduce several classes of operators: nonexpansive, quasi-nonexpansive, strictly quasi-nonexpansive, strongly quasi-nonexpansive, cutters, firmly nonexpansive, relaxed firmly nonexpansive and strongly nonexpansive. We present general properties of these operators, prove the closedness of these classes under some algebraic operations and present the properties of the subsets of fixed points of operators from these classes. The importance of these operators follows from the fact that they define algorithms for solving convex optimization problems. In one iteration of the algorithm an appropriate operator (called an algorithmic operator) defines an actualization of the current approximation of a solution of the convex optimization problem.

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    Andrzej Cegielski

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Cegielski, A. (2012). Algorithmic Operators. In: Iterative Methods for Fixed Point Problems in Hilbert Spaces. Lecture Notes in Mathematics, vol 2057. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30901-4_2

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