Remarks on p-cyclically monotone operators

Orestes Bueno; John Cotrina

doi:10.1080/02331934.2019.1636049

Remarks on p-cyclically monotone operators

Orestes Bueno, John Cotrina

Universidad del Pacífico

Research output: Contribution to journal › Article in a journal › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2071-2087
Number of pages	17
Journal	Optimization
Volume	68
Issue number	11
DOIs	https://doi.org/10.1080/02331934.2019.1636049
State	Published - 2 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

47H04
47H05
49J53
Brézis–Browder theorem
Fitzpatrick functions of order p
linear p-cyclically monotone operators
p-cyclically monotone operators

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10.1080/02331934.2019.1636049

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abstract = "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 Br{\'e}zis-Browder theorem preserves p-cyclical monotonicity in reflexive Banach spaces.",

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AU - Cotrina, John

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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

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U2 - 10.1080/02331934.2019.1636049

DO - 10.1080/02331934.2019.1636049

M3 - Article in a journal

VL - 68

SP - 2071

EP - 2087

JO - Optimization

JF - Optimization

SN - 0233-1934

IS - 11

ER -

Remarks on p-cyclically monotone operators

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