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Luke, D. Russell (author), Teboulle, Marc (author), Nguyen, Hieu Thao (author)We present necessary conditions for monotonicity of fixed point iterations of mappings that may violate the usual nonexpansive property. Notions of linear-type monotonicity of fixed point sequences—weaker than Fejér monotonicity—are shown to imply metric subregularity. This, together with the almost averaging property recently introduced by...journal article 2018