Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps

Abstract

We prove that the notions of -cyclic quasimonotonicity and -cyclic monotonicity are equivalent for affine maps defined on Banach spaces. First this is done in a finite dimensional space by using the index of asymmetry for matrices defined by J.-P. Crouzeix and C. Gutan. Then this equivalence is extended to general Banach spaces.