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Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

2 Issues per year

CiteScore 2017: 0.33

SCImago Journal Rank (SJR) 2017: 0.183
Source Normalized Impact per Paper (SNIP) 2017: 0.364

Mathematical Citation Quotient (MCQ) 2017: 0.27

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Volume 1, Issue 1


The Expected–Projection Method: Its Behavior and Applications to Linear Operator Equations and Convex Optimization

D. Butnariu
Published Online: 2010-06-03 | DOI: https://doi.org/10.1515/JAA.1995.93


It was shown by Butnariu and Flåm [J. Nnmer. Funct. Anal. Optim. 15: 601–636, 1995] that, under some conditions, sequences generated by the expected projection method (EPM) in Hilbert spaces approximate almost common points of measurable families of closed convex subsets provided that such points exist. In this work we study the behavior of the EPM in the more general situation when the involved sets may or may not have almost common points and we give necessary and sufficient conditions for weak and strong convergence. Also, we show how the EPM can be applied to finding solutions of linear operator equations and to solving convex optimization problems.

Key words and phrases.: Convex set; metric projection; Bochner integral; asymptotic center of sequence; stochastic convex feasibility problem; optimization problem

About the article

Published Online: 2010-06-03

Published in Print: 1995-06-01

Citation Information: Journal of Applied Analysis, Volume 1, Issue 1, Pages 93–108, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/JAA.1995.93.

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