On new majorization theorems
Several majorization theorems of the following type are proved: Let \(g\) be a strictly increasing function from \((a,b)\) to \((c,d)\), \(f\) be an increasing function on \((a,b)\) and \(f\circ g^{-1}\) be a concave function on \((c,d)\). If the vectors \({\mathbf x}\) and \({\mathbf y}\) with elements from \((a,b)\) satisfy \[ \sum_{i=1}^kw_ig(x_i)\geq\sum_{i=1}^kw_ig(y_i), \qquad k=1,\dots,n, \] and the vector \(\mathbf x\) is increasing, then \[ \sum_ {i=1}^kw_if(x_i)\geq\sum_{i=1}^kw_if(y_i),\qquad k=1,\dots,n. \] Some applications are also given.
scientific article; zbMATH DE number 1143475
scientific article