6 research outputs found
The Schur-Convexity of the Generalized Muirhead-Heronian Means
We give a unified generalization of the generalized Muirhead means and the generalized Heronian means involving three parameters. The Schur-convexity of the generalized Muirhead-Heronian means is investigated. Our main result implies the sufficient conditions of the Schur-convexity of the generalized Heronian means and the generalized Muirhead means
On Seiffert-like means
We investigate the representation of homogeneous, symmetric means in the form
M(x,y)=\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing
means. As an example, we provide optimal estimate of the form (1-\mu)min(x,y)+
\mu max(x,y)<= M(x,y)<= (1-\nu)min(x,y)+ \nu max(x,y) and
M((x+y)/2-\mu(x-y)/2,(x+y)/2+\mu(x-y)/2)<= N(x,y)<=
M((x+y)/2-\nu(x-y)/2,(x+y)/2+\nu(x-y)/2) for some known means
On Seiffert-like Means
We investigate the representation of homogeneous, symmetric means in the for