# Regular Sequences of Quasi-Nonexpansive Operators and Their Applications

arXiv: https://arxiv.org/abs/1710.00534 · HTML: https://mlsanity.com/paper/1710.00534/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems](https://mlsanity.com/paper/2408.12100/) (2024)

## Abstract (arXiv)

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 methods. 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.