Related papers: A new inequality for the Hermite constants
In this study, Firstly, we will write two new convex functions for $-1<n-\alpha \leq 1\ $and two new lemmas. Then we will find the relevance of the two new lemmas to Caputo-left-sided derivatives under additional conditions and draw…
In this paper, we study the stability of Minkowski inequality for nearly spherical domains that are $C^1$ close to the ball. We show the stability inequalities between the positive part of the $\sigma_k$ curvature integrals for $C^1$…
In this paper, we study the conjecture of Gardner and Zvavitch from \cite{GZ}, which suggests that the standard Gaussian measure $\gamma$ enjoys $\frac{1}{n}$-concavity with respect to the Minkowski addition of \textbf{symmetric} convex…
Let $M$ be an $n$-dimensional Lagrangian submanifold of a complex space form. We prove a pointwise inequality $$\delta(n_1,\ldots,n_k) \leq a(n,k,n_1,\ldots,n_k) \|H\|^2 + b(n,k,n_1,\ldots,n_k)c,$$ with on the left hand side any…
For an irrational real $\alpha$ and $\gamma\not \in \mathbb Z + \mathbb Z\alpha$ it is well known that $$ \liminf_{|n|\rightarrow \infty} |n| ||n\alpha -\gamma || \leq \frac{1}{4}. $$ If the partial quotients, $a_i,$ in the negative…
A conjecture of Pasteczka, generalizing the classical Hermite--Hadamard Inequality, states that if $\Omega \subseteq \mathbb{R}^d$ is a compact convex domain such that $\Omega$ and $\partial \Omega$ have the same center of mass, then for…
In literature the Hermite-Hadamard inequality was eligible for many reasons, one of the most surprising and interesting that the Hermite-Hadamard inequality combine the midpoint and trapezoid formulae in an inequality. In this work, a…
In this paper we consider a weighted version of one dimensional discrete Hardy's Inequality on half-line with power weights of the form $n^\alpha$. Namely we consider: \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq…
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…
We consider the $L^p$ Hardy inequality involving the distance to the boundary of a domain in the $n$-dimensional Euclidean space with nonempty compact boundary. We extend the validity of known existence and non-existence results, as well as…
Given an integer $m\geq2$, the Hardy--Littlewood inequality (for real scalars) says that for all $2m\leq p\leq\infty$, there exists a constant $C_{m,p}% ^{\mathbb{R}}\geq1$ such that, for all continuous $m$--linear forms…
Given any ${\bf{a}}: = \left( {a_1 ,a_2 , \ldots ,a_n } \right)$ and ${\bf{b}}: = \left( {b_1 ,b_2 , \ldots ,b_n } \right)$ in $\mathbb{R}^n$. The $\textbf{n}$-fold convex function defined on $\left[ {{\bf{a}},{\bf{b}}} \right]$,…
By use of a modified Nunokawa's lemma, we obtain some new conditions for univalence. Also, some sharp inequalities concerning univalent functions are presented.
A classical inequality due to Bohnenblust and Hille states that for every positive integer $m$ there is a constant $C_{m}>0$ so that $$(\sum\limits_{i_{1},...,i_{m}=1}^{N}|U(e_{i_{^{1}}},...,e_{i_{m}})| ^{\frac{2m}{m+1}})…
One of the best-known results in spectral graph theory is the inequality of Hoffman \[ \chi\left( G\right) \geq1-\frac{\lambda\left( G\right) }{\lambda_{\min }\left( G\right) }, \] where $\chi\left( G\right) $ is the chromatic number of a…
In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the…
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log…
In this paper we provide a new Bennequin-type inequality for the Rasmussen- Beliakova-Wehrli invariant, featuring the numerical transverse braid invariants (the c-invariants) introduced by the author. From the Bennequin type-inequality, and…
In this paper we study the fractional Caffarelli-Kohn-Nirenberg inequality (CKN) in one dimension when the parameter $\gamma$ converges (from the left) to its critical value $1/2$, obtaining Onofri's inequality in the unit disk as the…