Algorithm for Fixed Point Approximation of Fejer Operators

The theory of fixed points of operators and the corresponding algorithms are a powerful tool for studying nonlinear phenomena. The article considers the problems of finding fixed points of Fejer (quasi-nonexpansive) operators acting in Hilbert space, and variational inequalities on the set of fixed points. Strong convergence of the Halpern algorithm with averaging (the Halpern Suzuki algorithm) for finding fixed points of Fejer (quasi-nonexpansive) operators is proved.