Strong convergence theorems of modified Ishikawa iterations for countable hemi-relatively nonexpansive mappings in a Banach space.
We show that the set of those Markov semigroups on the Schatten class ₁ such that in the strong operator topology , where Q is a one-dimensional projection, form a meager subset of all Markov semigroups.
Let be a positive contraction, with . Assume that is analytic, that is, there exists a constant such that for any integer . Let and let be the space of all complex sequences with a finite strong -variation. We show that for any , the sequence belongs to for almost every , with an estimate . If we remove the analyticity assumption, we obtain an estimate , where denotes the ergodic average of . We also obtain similar results for strongly continuous semigroups of positive...
This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...
This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem...