Related papers: An equivalent form of Young's inequality with uppe…
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…
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…
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 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…
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…
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.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
We give a new proof of the sharp form of Young's inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than $1$. Our proof is…
We establish upper bounds for the convolution operator acting between interpolation spaces. This will provide several examples of Young Inequalities in different families of function spaces. We use this result to prove a bilinear…
We introduce a generalization of the Young integration on self-similar sets defined in a closed interval and give a sufficient condition of its integrability. We also prove integration by substitution, integration by parts and term-by-term…
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, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.
In this short note, we give the refined Young inequality with Specht's ratio by only elementary and direct calculations. The obtained inequality is better than one previously shown by the author in 2012. In addition, we give a new property…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
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.
Young's convolution inequality provides an upper bound for the convolution of functions in terms of $L^p$ norms. It is known that for certain groups, including Heisenberg groups, the optimal constant in this inequality is equal to that for…