Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces.
In this paper, the authors establish the result that the iteration scheme \(x_{n+1}=\lambda_{n+1}y+(1-\lambda_{n+1})T_{n+1}x_n\) for infinitely/finitely many nonexpansive mappings \(T_i\) in a Hilbert space converges to \(Py\), where \(P\) is the projection onto the intersection of the fixed point sets of the \(T_i\)'s. This generalizes the result of \textit{T. Shimizu} and \textit{W. Takahashi} [J. Math. Anal. Appl. 211, 71--83 (1997; Zbl 0883.47075)], a complementary result to a result of \textit{H.~H. Bauschke} [J. Math. Anal. Appl. 202, 150--159 (1996; Zbl 0956.47024)], by introducing a condition on the sequence of parameters (\(\lambda_n\)). This condition improves \textit{P.-L. Lions}' condition [C. R. Acad. Sci., Paris, Sér. A 284, 1357--1359 (1977; Zbl 0349.47046)].
scientific article; zbMATH DE number 1975873
scientific article