TY - JOUR
T1 - Remarks on p-cyclically monotone operators
AU - Bueno, Orestes
AU - Cotrina, John
N1 - Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/11/2
Y1 - 2019/11/2
N2 - In this paper, we deal with three aspects of p-cyclically monotone operators. First, we introduce a notion of monotone polar adapted for p-cyclically monotone operators and study these kinds of operators with a unique maximal extension (called pre-maximal), and with a convex graph. We then deal with linear operators and provide characterizations of p-cyclical monotonicity and maximal p-cyclical monotonicity. Finally, we show that the Brézis-Browder theorem preserves p-cyclical monotonicity in reflexive Banach spaces.
AB - In this paper, we deal with three aspects of p-cyclically monotone operators. First, we introduce a notion of monotone polar adapted for p-cyclically monotone operators and study these kinds of operators with a unique maximal extension (called pre-maximal), and with a convex graph. We then deal with linear operators and provide characterizations of p-cyclical monotonicity and maximal p-cyclical monotonicity. Finally, we show that the Brézis-Browder theorem preserves p-cyclical monotonicity in reflexive Banach spaces.
KW - 47H04
KW - 47H05
KW - 49J53
KW - Brézis–Browder theorem
KW - Fitzpatrick functions of order p
KW - linear p-cyclically monotone operators
KW - p-cyclically monotone operators
KW - 47H04
KW - 47H05
KW - 49J53
KW - Brézis–Browder theorem
KW - Fitzpatrick functions of order p
KW - linear p-cyclically monotone operators
KW - p-cyclically monotone operators
UR - http://www.scopus.com/inward/record.url?scp=85068562429&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/fea1aedb-825e-3360-923c-20c2b4ec843c/
U2 - 10.1080/02331934.2019.1636049
DO - 10.1080/02331934.2019.1636049
M3 - Article in a journal
SN - 0233-1934
VL - 68
SP - 2071
EP - 2087
JO - Optimization
JF - Optimization
IS - 11
ER -