The author gives a unified treatment of several well-known algorithms in signal processing and image reconstruction. These are special case of the Krasnoselskii-Mann iterative procedure [cf.

*W. R. Mann*, Proc. Am. Math. Soc. 4, 506–510 (1953;

Zbl 0050.11603)] to finding fixed points of nonexpansive continuous operators on Hilbert space. They include the Gerchberg-Papoulis method [cf.

*A. Papoulis*, IEEE Trans. Circuits and Systems CAS-22, No. 9, 735–742 (1975)] for bandlimited extrapolation, the SART algorithm of

*A. Anderson* and

*A. Kak* [Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm. Ultrason. Imaging 6, 81–94 (1984)], the Landweber and projected Landweber algorithm [cf.

*L. Landweber*, Am. J. Math. 73, 615–624 (1951;

Zbl 0043.10602)], simultaneous and sequential methods for solvig the convex feasibility problem, the ART and Cimmino methods [cf.

*G. Cimmino*, Ric. Sci. Progr. Tecn. Econom. Naz. 1, 326–333 (1938;

Zbl 0018.41802)]for solving linear systems of equations, the CQ algorithm for solving the split feasibility problem and

*Z. O. Dolidze*’s procedure [Ekonom. i Mat. Metody 18, No. 5, 925–929 (1982)] for the variational inequality problem for monotone operators.