Related papers: Young's integral inequality with upper and lower b…
In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two…
We prove a sharp analog of Young's inequality on $S^N$, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This…
In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.
The aim of this paper is to analyze the weighted KyFan inequality proposed in [11]. A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
In queueing theory, Lorden's inequality can be used for bounds estimation of the moments of backward and forward renewal times. Two random variables called backwards renewal time and forward renewal time for this process are defined.…
The goal of this paper is to give the necessary and sufficient condition for Banach function spaces on which Young's inequality holds. As an application, we consider the maximal regularity estimate of heat equations for Besov spaces…
In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.
In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein…
In this paper we prove that under weak conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p-variation norms, greedy time…
We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified…
This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…
We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.
We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a criterion for the non-positivity of it.…
We establish a new bound for the exponential sum \begin{eqnarray*} \sum_{x\in\mathcal{X}}\Big|\sum_{y\in \mathcal{Y}}\gamma(y)\exp(2\pi i a \lambda^{xy}/p)\Big|, \end{eqnarray*} where $\lambda$ is an element of the residue ring modulo a…