Regular Sequences of Quasi-Nonexpansive Operators and Their Applications [article]

Andrzej Cegielski, Simeon Reich, Rafał Zalas
2018 arXiv   pre-print
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of the regularity is preserved under relaxations, convex combinations and products of operators. Moreover, in this connection, we show that weak, bounded and linear regularity lead to weak, strong and linear convergence, respectively, of various iterative
more » ... . This applies, in particular, to block iterative and string averaging projection methods, which, in principle, are based on the above-mentioned algebraic operations applied to projections. Finally, we show an application of regular sequences of operators to variational inequality problems.
arXiv:1710.00534v2 fatcat:nvykrdwvcncvlbhatmmde55nci