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

• Autorzy: Radu Ioan Boţ , Sorin-Mihai Grad
• Języki publikacji: EN

Abstrakty

EN

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 when 0 belongs to the range of S + T. Several special cases are discussed, some of them delivering interesting byproducts.

Słowa kluczowe

EN

Conjugate functions; Subdifferentials; Representative functions; Maximal monotone operators; Surjectivity

Kategorie tematyczne

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 162-172

Daty

wydano

2011-02-01

online

2010-12-30

Twórcy

autor

Radu Ioan Boţ

• Heinrich-Heine University

autor

Sorin-Mihai Grad

• Chemnitz University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0083-7