doiSerbia

A chain of mean value inequalities

Alzer Horst, h.alzer@gmx.de
Kwong Man Kam (Hong Kong Polytechnic University Hunghom, Hong Kong), mankwong@connect.polyu.hk

G = G(x, y) = √xy, L = L(x,y) = x−y/log(x)−log(y)'' I=I(x,y)= 1/e(xx/yy) 1/(x-y), A=A(x.y)=x+y/2, be the geometric, logarithmic, identric, and arithmetic means of x and y. We prove that the inequalities L(G2,A2) < G(L2,I2) < A(L2,I2) < I(G2,A2) are valid for all x, y > 0 with x ≠ y. This refines a result of Seiffert.

Keywords: Mean values, inequalities