48 citations · 199 across the 83 of their papers we have counts for
10 papers · 2 filters
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…
The Brézis-Browder Theorem in a general Banach space
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
During the 1970s Brézis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend an…
Monotone operators and "bigger conjugate" functions
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
We study a question posed by Stephen Simons in his 2008 monograph involving "bigger conjugate" (BC) functions and the partial infimal convolution. As Simons demonstrated in his mon…
Construction of pathological maximally monotone operators on non-reflexive Banach spaces
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brøns…
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…
Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question po…
For maximally monotone linear relations, dense type, negative-infimum type, and Fitzpatrick-Phelps type all coincide with monotonicity of the adjoint
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick-Phelps t…
Maximally Monotone Linear Subspace Extensions of Monotone Subspaces: Explicit Constructions and Characterizations
Xianfu Wang, Liangjin Yao
Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace ex…
Fixed Points of Averages of Resolvents: Geometry and Algorithms
Heinz H. Bauschke, Xianfu Wang, Calvin J. S. Wylie
To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the…
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…