Kantorovich-type inequalities for operators via D-optimal design theory

Kantorovich type inequalities for ordered linear spaces

In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...

On Several Matrix Kantorovich-Type Inequalities

Optimal Hardy–littlewood Type Inequalities for Polynomials and Multilinear Operators

Abstract. In this paper we obtain quite general and definitive forms for Hardy–Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative a...

Optimal Weyl-type inequalities for operators in Banach spaces

Let (sn) be an s-number sequence. We show for each k = 1, 2, . . . and n ≥ k + 1 the inequality

About the Bivariate Operators of Kantorovich Type

The aim of this paper is to study the convergence and approximation properties of the bivariate operators and GBS operators of Kantorovich type.