A comparison theorem on generalized capacity

On a generalized Sturm theorem

Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm theorem for indefinite systems with Dirichlet boundary conditions of the form p2m du dx + p2m−2(x) du dx + · · ·+ p1(x) du dx + p0(x)u = 0, where pi is a smooth path of matrices on the comple...

On Generalized Stone’s Theorem

It is known that the generator of a strictly continuous one parameter unitary group in the multiplier algebra of a C∗ -algebra is affiliated to that C∗ -algebra . We show that under natural non degeneracy conditions, this self adjoint unbounded operator lies indeed in the (unbounded) multiplier algebra of the Pedersen’s ideal of the C∗ -algebra .

A Fixed Point Theorem in Generalized D-metric Spaces

A Generalized Cantor Theorem

A well known theorem of Cantor asserts that the cardinal of the power-set of a given set always exceeds the cardinal of the original set. An analogous result for sets having additional structure is the well known theorem that the set of initial segments of a well ordered set always has order type greater than the original set. These two theorems suggest that there should be a similar result for...

A Generalized Winternitz Theorem

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ∈ P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P . We also give a family of examples showing that this result is the best possible. Mathematics Subject Classification (2010). 51E99.