Regular Sequences of Quasi-Nonexpansive Operators and Their Applications

@article{Cegielski2017RegularSO,
  title={Regular Sequences of Quasi-Nonexpansive Operators and Their Applications},
  author={Andrzej Cegielski and Simeon Reich and Rafał Zalas},
  journal={SIAM J. Optim.},
  year={2017},
  volume={28},
  pages={1508-1532}
}
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… 

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