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2011 | 9 | 1 | 162-172
Tytuł artykułu

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

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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.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
1
Strony
162-172
Opis fizyczny
Daty
wydano
2011-02-01
online
2010-12-30
Twórcy
Bibliografia
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  • [5] Boţ R.I., Conjugate Duality in Convex Optimization, Lecture Notes in Econom. and Math. Systems, 637, Springer, Berlin, 2010
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  • [7] Boţ R.I., Wanka G., A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces, Nonlinear Anal., 2006, 64(12), 2787–2804. http://dx.doi.org/10.1016/j.na.2005.09.017
  • [8] Marques Alves M., Svaiter B.F., On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive Banach spaces, J. Convex Anal., 2011, 18(1), 209–226
  • [9] Martínez-Legaz J.-E., Some generalizations of Rockafellar's surjectivity theorem, Pac. J. Optim., 2008, 4(3), 527–535
  • [10] Moudafi A., Oliny M., Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math., 2003, 155(2), 447–454
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  • [12] Rocco M., Martínez-Legaz J.-E., On surjectivity results for maximal monotone operators of type (D), J. Convex Anal., 2011, 18(2) (in press)
  • [13] Rockafellar R.T., On the maximal monotonicity of subdifferential mappings, Pacific J. Math., 1970, 33(1), 209–216
  • [14] Simons S., From Hahn-Banach to Monotonicity, 2nd ed., Lecture Notes in Math., 1693, Springer, Berlin, 2008
  • [15] Zăalinescu C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 2002 http://dx.doi.org/10.1142/9789812777096
  • [16] Zălinescu C., A new convexity property for monotone operators, J. Convex Anal., 2006, 13(3–4), 883–887
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0083-7
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