Related papers: Inequalities related to the error function
A class of increasing sequences of natural numbers $(n_k)$ is found for which there exists a function $f\in L[0,1)$ such that the subsequence of partial Walsh-Fourier sums $(S_{n_k}(f))$ diverge everywhere. A condition for the growth order…
In the context of the Calculus of Variations for non-convex, vector variational problems, the natural process of going from a function $\phi$ to its quasiconvexification $Q\phi$ is quite involved, and, most of the time, an impossible task.…
A new transformation involving the error function $\textup{erf}(z)$, the imaginary error function $\textup{erfi}(z)$, and an integral analogue of a partial theta function is given along with its character analogues. Another complementary…
Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper error bounds of such…
We introduce new zeta functions related to an endomorphism $\phi$ of a discrete group $\Gamma$. They are of two types: counting numbers of fixed ($\rho\sim \rho\circ\phi^n$) irreducible representations for iterations of $\phi$ from an…
We identify a one-parameter family of inequalities for the Fourier transform whose limiting case is the restriction conjecture for the sphere. Using Stein's method of complex interpolation we prove the conjectured inequalities when the…
We present a weighted version of the Caffarelli-Kohn-Nirenberg inequality in the framework of variable exponents. The combination of this inequality with a variant of the fountain theorem, yields the existence of infinitely many solutions…
In this paper, we establish new irrationality criteria for certain sparse power series. As applications of these criteria, we generalize a result of Erd\H{o}s and obtain several irrationality results for various infinite series involving…
Katz and Sarnak conjectured a correspondence between the $n$-level density statistics of zeros from families of $L$-functions with eigenvalues from random matrix ensembles. In many cases the sums of smooth test functions, whose Fourier…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
For a family of infinite-dimensional diffusions with degenerate noise, we develop a modified $\Gamma$ calculus on finite-dimensional projections of the equation in order to produce explicit functional inequalities that can be scaled to…
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.
This paper is inspired by the work of J. S\'{a}ndor in 2006. In the paper, the authors establish some double inequalities involving the ratio $ \frac{\Gamma_{q}(x+1)}{ \Gamma_{q} \left( x+\frac{1}{2}\right)}$, where $\Gamma_{q}(x)$ is the…
Using the results of \cite{P1}, we get some estimates of warping functions for isometric immersions by changing the target manifolds by some types of Riemannian manifolds: constant space forms and Hermitian symmetric spaces. And we deal…
Inspired by a conjecture of Vladimir Maz'ya on $\Phi$-inequalities in the spirit of Bourgain and Brezis, we establish some $\Phi$-inequalities for fractional martingale transforms. These inequalities may be thought of as martingale models…
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…
Let $\beta>1$, $I$ be the unite interval $[0,1)$ and $\phi$ be an integer function defined on $\mathbb{N}\setminus\{0\}$ satisfying $1\leq\phi(n)\leq n$. Denote by $A_\phi(x,\beta)$ the Erd\"{o}s-R\'{e}nyi average of $x\in I$ associated…
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
In this note, we establish new an inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.