سال انتشار: ۱۳۸۶

محل انتشار: سی و هشتمین کنفرانس ریاضی ایران

تعداد صفحات: ۳

نویسنده(ها):

J ROOIN – Department of Pure Mathematics, Institute for Advanced Studies, In Basic Sciences 45195-1159, zanjan, Iran
A MORASSAEL – Department of Pure Mathematics, Faculty of Science, University Of zanjan 45195-1-313, and Education Office of zanjan, iran

چکیده:

Let (X, A,μ) and (Y, B, λ) be two probability measore spaces, I an interval of the real line, f Є L1(μ), f(x) Є I for each x Є X, and φ a realvalued convex function on I. We show that, if w0 and w1 are two appropriate weight functions on X*Y, then
φ(∫xfdμ) ≤ ∫Y A(φ, F0(y), F1(y)) dλ(y) ≤∫x (φ f) dμ
where A denotes the arthmetic mean of φ over the closed interval with end points F0(y), and for λ-almost all yЄY’s
Fk(y) = ∫x f(x) wk(x,y)dμ (x)(k=0,1).
At the end, we give some nice applications refining AGM and the information inequalities.