Open AccessA chain of mean value inequalities
Author(s) -
Horst Alzer,
Man Kwong Kam
Publication year - 2020
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm190718027a
Subject(s) - mathematics , combinatorics , logarithm , value (mathematics) , chain (unit) , mathematical analysis , physics , statistics , astronomy
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)0 with x ? y. This refines a result of Seiffert.