Boundary regularity and sufficient conditions for strong local minimizers

New necessary conditions for Lipschitz strong local minimizers

We derive a set of new necessary conditions for Lipschitz strong local minimizers. These conditions restrict the behavoir of the L gradient of the minimizer at its discontinuities. We show by way of examples that the derived conditions are independent of one another.

Sufficient conditions for univalence and starlikeness

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

Strong Topological Regularity and Weak Regularity of Banach Algebras

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

New sufficient conditions for strong simultaneous stabilization

In this brief paper we present sufficient conditions for the existence of a single stable controller to stabilize a set of n SISO plants: P1, P2, ..., Pn (strong simultaneous stabilization). As is well known this is equivalent to the existence of a single controller, not necessarily stable, to stabilize n+1 plants (simultaneous stabilization). The basic assumption required in the current paper ...

Partial regularity for quasi minimizers