Reverses and variations of Young's inequalities with Kantorovich constant

Improvements of Young inequality using the Kantorovich constant

‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

New progress on the operator inequalities involving improved Young’s and its reverse inequalities relating to the Kantorovich constant

The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young's and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young's inequalities are promoted, the operator version and the Hilbert-Schmidt form ...

On Several Matrix Kantorovich-Type Inequalities

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...

Hadamard Product Versions of the Chebyshev and Kantorovich Inequalities

The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler’s inequality.