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Luke, D. Russell (author), Nguyen, Hieu Thao (author), Tam, Matthew K. (author)We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point...journal article 2018
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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