Necessary and sufficient conditions on the Schur convexity of a bivariate mean

Abstract

In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.

Keywords

• necessary and sufficient condition
• bivariate mean
• schur convex function
• schur harmonically convex function
• inequality
• majorization