Remarks on p-cyclically monotone operators

@article{Bueno2017RemarksOP,
  title={Remarks on p-cyclically monotone operators},
  author={Orestes Bueno and John Edwin Cotrina},
  journal={Optimization},
  year={2017},
  volume={68},
  pages={2071 - 2087}
}
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… 
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On the construction of maximal $p$-cyclically monotone operators

In this paper we deal with the construction of explicit examples of maximal $p$-cyclically monotone operators. To date, there is only one instance of an explicit example of a maximal 2-cyclically…

References

SHOWING 1-10 OF 14 REFERENCES

Monotone Operators Representable by l.s.c. Convex Functions

A theorem due to Fitzpatrick provides a representation of arbitrary maximal monotone operators by convex functions. This paper explores representability of arbitrary (nonnecessarily maximal) monotone…

An explicit example of a maximal 3-cyclically monotone operator with bizarre properties

A remark on the Brézis–Browder theorem in finite dimensional spaces

Abstract Brézis and Browder gave an important characterization of maximal monotonicity for linear operators, in reflexive Banach spaces. In this paper, we show that this characterization also…

Linear Maximal Monotone Operators and Singular Nonlinear Integral Equations of Hammerstein Type

On Maximality of Quasimonotone Operators

We introduce the notion of quasimonotone polar of a multivalued operator, in a similar way as the well-known monotone polar due to Martínez-Legaz and Svaiter. We first recover several properties…

The Brezis–Browder Theorem in a general Banach space

Monotone Linear Relations: Maximality and Fitzpatrick Functions

We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained…

Maximal Monotone Operators with a Unique Extension to the Bidual

We present a new sufficient condition under which a maximal monotone operator $T:X\tos X^*$ admits a unique maximal monotone extension to the bidual $\widetilde T:X^{**} \rightrightarrows X^*$. For…

Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative

The pseudomonotone polar for multivalued operators

In this work, we study the pseudomonotonicity of multivalued operators from the point of view of polarity, in an analogous way as the well-known monotone polar due to Martínez-Legaz and Svaiter, and…