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摘要
The main objective of the present paper, is to obtain some new versions of Young-type inequalities with respect to two weighted arithmetic and geometric means and their reverses, using two inequalities
K(b/a,2)(r )<= a del nu b/a#nu b <= K(b/a,2)(R),
where r = min{ nu, 1 - nu}, R = max {nu,1 - nu} and K(t,2) = (t+ 1)(2)/4t is the Kantorovich constant, and
e(h(-1),nu) <= a del nu b/a#nu b <= e(h,v),
where h = max{ a/b, b/a} and e(t, v) = exp (4 nu(1 - nu)(K(t, 2) - 1)(1 - 2t)). Also some operator versions of these inequalities and some inequalities related to Heinz mean are proved.
- 出版日期2018-8
