On Fixed Point Properties of a Convex Combination of Metric Projections

Abstract

To illustrate the usability of a famous Browder's theorem, some fixed point properties of a convex combination of metric projections are provided.

Contact details are reproduced from the original publication and may be historical.

Dept. of Mathematics, Valahia University, Bd. Unirii 18, 130024 Targoviste, Romania

Dept. of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al-Khod, Muscat, Sultanate of Oman

47H09, 47H10

H. Bauschke, J. Borwein: On projection algorithms for solving convex feasibility problems, SIAM Rev. 38(3) (1996) 367–426https://doi.org/10.1137/S0036144593251710 Google Scholar
F. E. Browder: Nonexpansive nonlinear operators in Banach spaces, Proc. Natl. Acad. Sci. USA 54 (1965) 1041–1044.https://doi.org/10.1073/pnas.54.4.1041 Google Scholar
A. Cegielski: A generalization of the Opial’s theorem, Control Cybern 36(3) (2007) 601–610.Google Scholar
A. Cegielski: Methods for finding fixed points of nonexpansive operators in a Hilbert space, IfMPreprint No. M 08/20, Technische Universität Ilmenau (2008).Google Scholar
A. Cegielski, R. Zalas: Methods for variational inequality problem over the intersection of fixed point sets of quasi-nonexpansive operators, Numer. Func. Anal. Optim. 34(3) (2013) 255–283.https://doi.org/10.1080/01630563.2012.716807 Google Scholar
G. Crombez: Image recovery by convex combinations of projections, J. Math. Anal. Appl. 155(2) (1991) 413–419.https://doi.org/10.1016/0022-247X(91)90010-W Google Scholar

Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.