# Cited predecessor check

Checked 2026-09-14 by the primary Zerone development assistant. This is an
internal source check, not externally independent review or an audit of Song's
whole paper.

Yanlai Song, *Iterative methods for fixed point problems and generalized split
feasibility problems in Banach spaces*, J. Nonlinear Sci. Appl. 11 (2018),
198–217, DOI [10.22436/jnsa.011.02.03](https://isr-publications.com/jnsa/articles-6677-iterative-methods-for-fixed-point-problems-and-generalized-split-feasibility-problems-in-banach-spaces),
is reference 41 of the PLOS article.

Song's Lemma 2.5 (pp. 202–203) gives quasi-nonexpansiveness of a suitably relaxed
demimetric map. Lemma 3.3 (p. 204) specifies positive weights summing to one and
gives demimetricity and the common-fixed-point identity for their average. It
does not assert pairwise nonexpansiveness. In the proof of Theorem 3.4 (p. 208),
a weighted residual inner-product estimate yields individual residual
convergence; the assumed demiclosedness of the original maps then identifies
the weak limit. This is an existing antecedent for the proposed residual-based
repair, not a novelty claim. It does not settle every assumption or inference in
the later PLOS article.

The publisher PDF was retained locally for reading, with SHA-256
`afcbc03363ad813be6f8834117de1d9c99f4cd52fc1e6c66ad7ce46232fc9d6a`.
See `SOURCES.json` for the source inventory; the original fetch receipt is retained privately. Printed pp. 204 and 208 were rendered and visually checked
against extracted text. The full PDF and page renders are not included in the
shareable packet; recipients can consult the publisher. No article code ran.