TY - JOUR
A2 - Hajja, Mowaffaq
AU - Simic, Slavko
PY - 2013
DA - 2013/02/12
TI - On Some Intermediate Mean Values
SP - 283127
VL - 2013
AB - We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class Λf,g(a,b) of mean values where f,g are continuously differentiable convex functions satisfying the relation f″(t)=tg″(t), t∈ℝ+. Then we asked for a characterization of f,g such that the inequalities H(a,b)≤Λf,g(a,b)≤A(a,b) or L(a,b)≤Λf,g(a,b)≤I(a,b) hold for each positive a,b, where H,A,L,I are the harmonic, arithmetic, logarithmic, and identric means, respectively. For a subclass of Λ with g″(t)=ts, s∈ℝ, this problem is thoroughly solved.
SN - 0161-1712
UR - https://doi.org/10.1155/2013/283127
DO - 10.1155/2013/283127
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi Publishing Corporation
KW -
ER -