Related papers: Some refinements of classical inequalities
In this paper, we study refinements of some inequalities related to Young inequality for scalar and for operator. As our main results, we show refined Young inequalities for two positive operators. This results refine the ordering relations…
In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two…
In this note, some refinements of Young inequality and its reverse for positive numbers are proved and using these inequalities some operator versions and Hilbert-Schmidt norm versions for matrices of these inequalities are obtained.
In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…
In this paper, sharp results on operator Young's inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young's inequality. Secondly, we give an additive result, which improves a well-known…
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…
In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between…
In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
Jensen's operator inequality for convexifiable functions is obtained. This result contains classical Jensen's operator inequality as a particular case. As a consequence, a new refinement and a reverse of Young's inequality is given.
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange's and Cauchy's type remainders, and via several fundamental…
We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the…
In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are…
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…