We prove in this article using some convex analysis results of A. S. Lewis the log-concavity of spectral elementary symmetric functions on the space of Hermitian matrices, and the convexity of the set of k-admissible functions on compact Kähler manifolds.

Finally we wish to indicate that a procedure analogous to those of [4] enables us to associate with every function/, meromorphic in 9JÎ, a characteristic function T(r, ƒ), r<\. Using the results of [5] and those of a work of Bers as well as the theorem of this paper it is possible to show that, under certain hypotheses, |jf| possesses boundary values almost everywhere on g, if the T(r, ƒ) is un...

In the unit ball B(0, 1), let u and Ω (a domain in RN ) solve the following overdetermined problem: ∆u = χΩ in B(0, 1), 0 ∈ ∂Ω, u = |∇u| = 0 in B(0, 1) \ Ω, where χΩ denotes the characteristic function, and the equation is satisfied in the sense of distributions. If the complement of Ω does not develop cusp singularities at the origin then we prove ∂Ω is analytic in some small neighborhood of t...

In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore,  the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some  characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtai...

Given the n x p orthogonal matrix A and the convex function f : R"-~ R, we find two orthogonal matrices P and Q such that f is almost constant on the convex hull of ± the columns of P, f is sufficiently nonconstant on the column space of Q, and the column spaces of P and Q provide an orthogonal direct sum decomposi t ion of the column space of A. This provides a numerical ly stable algorithm fo...

In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in a normed space. By using this characterization we obtain, as a natural consequence, the formula for the biconjugate of the pointwise maximum of two functions, provided the so-call...

We denote the numerical range of the normal operator T by W (T). A characterization is given to the points inW (T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W (T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, s...

The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the fol...

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