Related papers: Young's integral inequality with upper and lower b…
The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
In this survey we consider generalizations for Young and Cauchy--Bunyakowsky inequalities with applications.
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…
The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2020}, is to propose several new inequalities for the function $y=t\ln t.$ We consider the local behaviour of this function near the point $t=1,$ as…
A quadratic inequality is formulated in the paper. An estimate on the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations.
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.
We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first…
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
Our main result is an abstract good-$\lambda$ inequality that allows us to consider three self-improving properties related to oscillation estimates in a very general context. The novelty of our approach is that there is one principle…
This work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs $(u_j,Du_j)j$ for $(u_j)_j \in \mathrm{BV}(\Omega;\mathbb{R}^m)$ under weak* convergence. These tools are…
Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
Improved model independent upper bounds on the weak transition form factors are derived using inclusive sum rules. Comparison of the new bounds with the old ones is made for the form factors h_{A_1} and h_V in B -> D* decays.
In this paper we present some new upper bounds of the Cusa-Huygens and the Huygens approximations. Bounds are obtained in the forms of some polynomial and some rational functions.
We present two extensions of the one dimensional free Poincar\'e inequality similar in spirit to two classical refinements.
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the…