Further generalization, refinements of the Young inequality

Generalization of cyclic refinements of Jensen’s inequality by Fink’s identity

We generalize cyclic refinements of Jensen’s inequality from a convex function to a higher-order convex function by means of Lagrange–Green’s function and Fink’s identity. We formulate the monotonicity of the linear functionals obtained from these identities utilizing the theory of inequalities for n-convex functions at a point. New Grüssand Ostrowski-type bounds are found for identities associ...

Refinements of Pinsker's inequality

Let V and D denote, respectively, total variation and divergence. We study lower bounds of D with V fixed. The theoretically best (i.e. largest) lower bound determines a function L = L(V ), Vajda’s tight lower bound, cf. Vajda, [?]. The main result is an exact parametrization of L. This leads to Taylor polynomials which are lower bounds for L, and thereby extensions of the classical Pinsker ine...

Refinements of Generalized Hölder’s Inequality

In this paper, we present some refinements of a generalized Hölder’s inequality, which is due to Vasić and Pečarić. Mathematics subject classification (2010): Primary 26D15; Secondary 26D10.

Refinements of Kantorovich Inequality for Hermitian Matrices

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...