Kato’s inequality is shown for the magnetic relativistic Schrödinger operator HA,m defined as the operator theoretical square root of the selfadjoint, magnetic nonrelativistic Schrödinger operator (−i∇−A(x))2 +m2 with an Lloc vector potential A(x). Mathematics Subject Classification (2010): 47A50; 81Q10; 47B25; 47N50; 47D06; 47D08.

We design a new feedback law to stabilize the linear infinite-dimensional control system, where state operator generates $ C_0 $-group, and is unbounded. Our based on integration of mutated Gramian operator-valued function. In structure aforementioned operator, we utilize weak observability inequality in [21,13] borrow some idea used construct generalized operators [11,23,24]. Unlike most relat...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

Korn’s inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its tr...

Birandom variable is a generalization of random variable, which is defined as a measurable function from a probability space to the set of random variables. In order to further explore the mathematical properties of birandom variable, this paper first investigates several inequalities for birandom variables based on the chance measure and expected value operator, which are analogous to Hölder’s...

As Schneider [50] observes, the classical Brunn-Minkowski theory had its origin at the turn of the 19th into the 20th century, when Minkowski joined a method of combining convex bodies (which became known as Minkowski addition) with that of ordinary volume. One of the core concepts that Minkowski introduced within the Brunn-Minkowski theory is that of projection body (precise definitions to fol...

In this paper, we present a version of horizontal weighted Hardy–Rellich type and Caffarelli–Kohn– Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale–Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also s...

We analyze the level sets of the norm of the Witten spinor in an asymptotically flat Riemannian spin manifold of positive scalar curvature. Level sets of small area are constructed. We prove curvature estimates which quantify that, if the total mass becomes small, the manifold becomes flat with the exception of a set of small surface area. These estimates involve either a volume bound or a spec...

This paper concerns with rank-dependent poverty measures and shows that an ordered weighted averaging, hereafter OWA, operator is underlying in the definition of these indices. The dual decomposition of an OWA operator into the self-dual core and the anti-self-dual remainder allows us to propose a decomposition for all the rank-dependent poverty measures in terms of incidence, intensity and ine...