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

Radu Ioan Boţ; Sorin-Mihai Grad

Open Mathematics (2011)

  • Volume: 9, Issue: 1, page 162-172
  • ISSN: 2391-5455

Abstract

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

How to cite

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Radu Ioan Boţ, and Sorin-Mihai Grad. "Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators." Open Mathematics 9.1 (2011): 162-172. <http://eudml.org/doc/269788>.

@article{RaduIoanBoţ2011,
abstract = {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.},
author = {Radu Ioan Boţ, Sorin-Mihai Grad},
journal = {Open Mathematics},
keywords = {Conjugate functions; Subdifferentials; Representative functions; Maximal monotone operators; Surjectivity; conjugate functions; subdifferentials; representative functions; maximal monotone operators; surjectivity},
language = {eng},
number = {1},
pages = {162-172},
title = {Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators},
url = {http://eudml.org/doc/269788},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Radu Ioan Boţ
AU - Sorin-Mihai Grad
TI - Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators
JO - Open Mathematics
PY - 2011
VL - 9
IS - 1
SP - 162
EP - 172
AB - 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.
LA - eng
KW - Conjugate functions; Subdifferentials; Representative functions; Maximal monotone operators; Surjectivity; conjugate functions; subdifferentials; representative functions; maximal monotone operators; surjectivity
UR - http://eudml.org/doc/269788
ER -

References

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