When (M,ω, μ : M → U) is a quasi-hamiltonian U -space with U a compact connected and simply connected Lie group, the intersection of μ(M) with the exponential exp(W) of a closed Weyl alcove W ⊂ u = Lie(U) is homeomorphic, via the exponential map, to a convex polytope of u ([AMM98]). In this paper, we fix an involutive automorphism τ of U such that the involution τ− : u 7→ τ(u) leaves a maximal ...

In 1957 Chandler Davis proved a theorem that a rotationally invariant function on symmetric matrices is convex if and only if it is convex on the diagonal matrices. We generalize this result to groups acting nonlinearly on convex subsets of arbitrary vector spaces thereby understanding the abstract mechanism behind the classical theorem. We apply the new theorem to a problem from the mathematic...

The purpose of the present article is to study and introduce family holomorphic univalent functions defined on open unit disk incluing linear operators reduced by using convolution concept between two familiar introduced many authors also studied in various families generalized starlike convex functions. Also, mathematicians considered these families, our deals with Bord distribution series, we...

The distance from the convex hull of the range of an n-dimensional vector-valued measure to the range of that measure is no more than an/2, where a is the largest (one-dimensional) mass of the atoms of the measure. The case a = 0 yields Lyapounov's Convexity Theorem; applications are given to the bisection problem and to the bang-bang principle of optimal control theory.

This paper partially extends the f -core equivalence theorem of Hammond, Kaneko and Wooders (1989) for continuum economies with widespread externalities — i.e., those over which each individual has negligible control. Externalities need not result directly from trading activities. Neither free disposal of divisible goods nor monotone preferences are assumed. Instead, a slightly strengthened for...

The weighted matroid intersection problem has recently been extended to the valuated matroid intersection problem: Given a pair of valuated matroids Mi = (V,Bi, ωi) (i = 1, 2) defined on a common ground set V , find a common base B ∈ B1∩B2 that maximizes ω1(B)+ω2(B). This paper develops a Fenchel-type duality theory related to this problem with a view to establishing a convexity framework for n...