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Weaker constraint qualifications in maximal monotonicity. (English) Zbl 1119.47051

The authors give a sufficient condition (involving the Fitzpatrick function) for the maximal monotonicity of the operator \(S+T\), where \(S:X\to 2^{X^*}\), \(T:X\to 2^{X^*}\) are two maximal monotone operators and \(X\) is a reflexive Banach space.
In a nonreflexive Banach space \(Y\), a condition for the Brézis–Haraux-type approximation of the range of the sum of two subdifferentials \(\partial f\) and \(\partial g\) (here, \(f,g:Y\to\overline{\mathbb R}\) are proper, convex, lower-semicontinuous functions) is also presented, extending and correcting a result of H.Riahi [Proc.Am.Math.Soc.124, No.11, 3333–3338 (1996; Zbl 0865.47037)].

MSC:

47H05 Monotone operators and generalizations
42A50 Conjugate functions, conjugate series, singular integrals
90C25 Convex programming

Citations:

Zbl 0865.47037
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References:

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