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We study a fixed point iterative method based on generalized relaxation ofstrictly quasi-nonexpansive operators. The iterative method is assembled byaveraging of strings, and each string is composed of finitely many strictlyquasi-nonexpansive operators. To evaluate the study, we examine a wide class ofiterative methods for solving linear systems of equations (inequalities) andthe subgradient projection method for solving nonlinear convex feasibilityproblems. The mathematical analysis is complemented by some experiments inimage reconstruction from projections and classical examples, which illustratethe performance using generalized relaxation.

A string averaging method based on strictly quasi-nonexpansive operators with generalized relaxation