Equivalence between the p-cyclic quasimonotonicity and the p-cyclic monotonicity for affine maps.

Resumen:

It is well known that, for general multivalued operators, monotonicity implies quasimonotonicity. This is also true if we deal with cyclic monotone/quasimonotone or even p-cyclic monotone/quasimonotone operators. In this work, we prove, in general Banach spaces, that an affine p-cyclic quasimonotone operator is in fact p-cyclic monotone.