QUADRATIC REFINEMENTS OF YOUNG TYPE INEQUALITIES

In this paper, we mainly give some quadratic refinements of Young type inequalities. Namely: (va + (1 - v)b)2 - v Sigma(N)(j=1)2(j) (b - (2j)root ab(2j-1))(2) <= (a(v)b(1-v))(2) + v(2)(a -b)(2) for v is not an element of [0, 1/2(N+1)], N is an element of N, a, b > 0; and (va + (1 - v)b)(2) - (1 - v) Sigma(N)(j=1)2j (a - (2j)root a(2j-1)b)(2) <= (a(v)b(1-v))(2) + (1 - v)(2) (a - b)(2) for v is not an element of [1 - 1/2(N+1), 1], N is an element of N, a, b > 0. As an application of these scalars results, we obtain some matrix inequalities for operators and Hilbert-Schmidt norms. (C) 2020 Mathematical Institute Slovak Academy of Sciences