On maximal monotone operators with relatively compact range
Czechoslovak Mathematical Journal (2010)
- Volume: 60, Issue: 1, page 105-116
- ISSN: 0011-4642
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topZagrodny, Dariusz. "On maximal monotone operators with relatively compact range." Czechoslovak Mathematical Journal 60.1 (2010): 105-116. <http://eudml.org/doc/37993>.
@article{Zagrodny2010,
abstract = {It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence of maximal monotone operators of type NI, which converge to $T$ in a reasonable sense (in the sense of Kuratowski-Painleve convergence).},
author = {Zagrodny, Dariusz},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear operators; maximal monotone operators; range of maximal monotone operator; an approximation method of maximal monotone operators; nonlinear operator; maximal monotone operator; range; maximal monotone operator; approximation method; maximal monotone operator},
language = {eng},
number = {1},
pages = {105-116},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On maximal monotone operators with relatively compact range},
url = {http://eudml.org/doc/37993},
volume = {60},
year = {2010},
}
TY - JOUR
AU - Zagrodny, Dariusz
TI - On maximal monotone operators with relatively compact range
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 105
EP - 116
AB - It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence of maximal monotone operators of type NI, which converge to $T$ in a reasonable sense (in the sense of Kuratowski-Painleve convergence).
LA - eng
KW - nonlinear operators; maximal monotone operators; range of maximal monotone operator; an approximation method of maximal monotone operators; nonlinear operator; maximal monotone operator; range; maximal monotone operator; approximation method; maximal monotone operator
UR - http://eudml.org/doc/37993
ER -
References
top- Debrunner, H., Flor, P., 10.1007/BF01589229, Arch. Math. 15 (1964), 445-447 German. (1964) Zbl0129.09203MR0170189DOI10.1007/BF01589229
- Fitzpatrick, S. P., Phelps, R. R., 10.1016/S0294-1449(16)30230-X, Ann. Inst. Henri Poincaré 9 (1992), 573-595. (1992) Zbl0818.47052MR1191009DOI10.1016/S0294-1449(16)30230-X
- Holmes, R. B., Geometric Functional Analysis and its Applications, Springer New York (1975). (1975) Zbl0336.46001MR0410335
- Phelps, R. R., Lecture on maximal monotone operators, Lecture given at Prague/Paseky, Summer school, arXiv:math/9302209v1 [math.FA] (1993). (1993) MR1627478
- Phelps, R. R., Convex Functions, Monotone Operators and Differentiability. Lecture Notes in Mathematics 1364, Springer Berlin (1989). (1989) MR0984602
- Rockafellar, R. T., 10.1007/BF01359698, Math. Ann. 185 (1970), 81-90. (1970) Zbl0181.42202MR0259697DOI10.1007/BF01359698
- Rudin, W., Functional Analysis (2nd edition), McGraw-Hill New York (1991). (1991) MR1157815
- Simons, S., From Hahn-Banach to Monotonicity. Lecture Notes in Mathematics 1693 (2nd expanded ed.), Springer Berlin (2008). (2008) MR2386931
- Simons, S., Minimax and Monotonicity. Lecture Notes in Mathematics 1693, Springer Berlin (1998). (1998) MR1723737
- Zagrodny, D., 10.1007/s11228-008-0087-7, Set-Valued Anal. 16 (2008), 759-783. (2008) Zbl1173.47031MR2465516DOI10.1007/s11228-008-0087-7
- Zeidler, E., Nonlinear Functional Analysis and its Applications, II/B: Nonlinear Monotone Operators, Springer Berlin (1990). (1990) Zbl0684.47029MR1033498
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