Displaying similar documents to “Abstract Subdifferential Calculus and Semi-Convex Functions”

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

Radu Ioan Boţ, Sorin-Mihai Grad (2011)

Open Mathematics

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In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation...

The cancellation law for inf-convolution of convex functions

Dariusz Zagrodny (1994)

Studia Mathematica

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Conditions under which the inf-convolution of f and g f □ g ( x ) : = i n f y + z = x ( f ( y ) + g ( z ) ) has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions f : X → ℝ ∪ + ∞ on a reflexive Banach space such that l i m ∥ x ∥ → ∞ f ( x ) / ∥ x ∥ = ∞ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.

Lectures on maximal monotone operators.

R. R. Phelps (1997)

Extracta Mathematicae

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These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces.

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Liana Cioban, Ernö Csetnek (2013)

Open Mathematics

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Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ...

Variational Principles for Monotone and Maximal Bifunctions

Chbani, Zaki, Riahi, Hassan (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05 We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.