Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings

DOI10.1090/S0002-9939-06-08770-3zbMath1181.49017MaRDI QIDQ3419980

Heinz H. Bauschke

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Fenchel dualityfirmly nonexpansive mappingFitzpatrick functionKirszbraun-Valentine theorem

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Fixed-point theorems (47H10) Convex functions and convex programs in convex geometry (52A41)

Related Items (16)

Continuity of extensions of Lipschitz maps ⋮ A new condition for maximal monotonicity via representative functions ⋮ Autoconjugate representers for linear monotone operators ⋮ Fixed point theorems for an elastic nonlinear mapping in Banach spaces ⋮ Proximal penalty-duality algorithms for mixed optimality conditions ⋮ On the generalized parallel sum of two maximal monotone operators of Gossez type (D) ⋮ Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality ⋮ Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection ⋮ Continuous extension operators and convexity ⋮ Convergence theorems for a maximal monotone operator and a \(V\)-strongly nonexpansive mapping in a Banach space ⋮ A convex-analytical approach to extension results for \(n\)-cyclically monotone operators ⋮ Fixed-point algorithms for frequency estimation and structured low rank approximation ⋮ About the maximal monotonicity of the generalized sum of two maximal monotone operators ⋮ Enlargements of positive sets ⋮ The kernel average for two convex functions and its application to the extension and representation of monotone operators ⋮ Kirszbraun’s Theorem via an Explicit Formula

Cites Work

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