# Fej'er monotone sequences revisited

arXiv: https://arxiv.org/abs/2310.06528 · HTML: https://mlsanity.com/paper/2310.06528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2023.

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

- [An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation](https://mlsanity.com/paper/2504.12922/) (2025)

## Abstract (arXiv)

In this paper we introduce a localized and relativized generalization of the usual concept of Fej'er monotonicity together with uniform and quantitative versions thereof and show that the main quantitative results obtained by the 1st author together with Nicolae and Leucstean in 2018 and with L'opez-Acedo and Nicolae in 2019 respectively, extend to this generalization. Our framework, in particular, covers the sequence generated by the Dykstra algorithm while the latter is not Fej'er-monotone in the ordinary sense. This gives a theoretical explanation why under a metric regularity assumption one obtains an explicit rate of convergence for Dykstra's algorithm which was proved recently by the 2nd author.