A hybrid iterative scheme for variational inequality problems for finite families of relatively weak quasi-nonexpansive mappings.
Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.
We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear...
Given a nonlinear autonomous system of ordinary or partial differential equations that has at least local existence and uniqueness, we offer a linear condition which is necessary and sufficient for existence to be global. This paper is largely concerned with numerically testing this condition. For larger systems, principals of computations are clear but actual implementation poses considerable challenges. We give examples for smaller systems and discuss challenges related to larger systems. This...
Given a strongly continuous semigroup on a Banach space X with generator A and an element f ∈ D(A²) satisfying and for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.
This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...
The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.