Majorization theorem for convexifiable functions

Majorization for A Subclass of β-Spiral Functions of Order α Involving a Generalized Linear Operator

Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk U. For this class, a majorization problem of analytic functions is discussed.

Four applications of majorization to convexity in the calculus of variations

The resemblance between the Horn-Thompson theorem and a recent theorem by Dacorogna-Marcellini-Tanteri indicates that Schur convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity, such as rank-one convexity or quasiconvexity. We give in theorem 6.6 simple necessary and sufficient conditions for an isotropic object...

Double-null operators and the investigation of Birkhoff's theorem on discrete lp spaces

Doubly stochastic matrices play a fundamental role in the theory of majorization. Birkhoff's theorem explains the relation between $ntimes n$ doubly stochastic matrices and permutations. In this paper, we first introduce double-null  operators and we will find some important properties of them. Then with the help of double-null operators, we investigate Birkhoff's theorem for descreate $l^p$ sp...

Linear preserving gd-majorization functions from Mn,m to Mn,k

Stochastic Orders and Majorization of Mean Order Statistics

We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected ...