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Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular
Heinz H. Bauschke, Victoria Martin-Marquez, Sarah M. Moffat +1
Because of Minty's classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of b…
Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main r…
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone…
Self-dual Smooth Approximations of Convex Functions via the Proximal Average
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
The proximal average of two convex functions has proven to be a useful tool in convex analysis. In this note, we express Goebel's self-dual smoothing operator in terms of the proxi…
The Resolvent Average for Positive Semidefinite Matrices
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interp…