Some Improvements of the Hermite–Hadamard Integral Inequality

On Some Improvements of the Jensen Inequality with Some Applications

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...

Some Extensions of Hilbert’s Integral Inequality

In this paper we introduce a new extension of Hilbert's integral inequality with a best constant factor involving the hypergeometric function. The equivalent form and some examples will be given.

Some new generalizations of Hardy's integral inequality

We have studied some new generalizations of Hardy's integral inequality using the generalized Holder's inequality.

Some Applications of the Isoperimetric Inequality for Integral Varifolds

In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón’s and Zygmund’s theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.