New explicit counterexamples demonstrate that Cesàro means of firmly nonexpansive iterates fail to converge strongly, remaining bounded away or oscillating in norm, in infinite-dimensional Hilbert spaces.
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Regularity of closed convex set pairs in Hilbert space is equivalent to variational stability of alternating projections, without boundedness assumptions on best approximation sets.
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Ces\`aro means of firmly nonexpansive iterates need not converge strongly
New explicit counterexamples demonstrate that Cesàro means of firmly nonexpansive iterates fail to converge strongly, remaining bounded away or oscillating in norm, in infinite-dimensional Hilbert spaces.
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Characterization of regularity via variational stability of alternating projections sequences
Regularity of closed convex set pairs in Hilbert space is equivalent to variational stability of alternating projections, without boundedness assumptions on best approximation sets.