Related papers: Some companions of perturbed Ostrowski type inequa…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we produce discrete fractional Taylor formulae for the first time, and we estimate their…
In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality,…
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…
Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed…
When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behaviour of the modified orthogonal polynomials is expected to have different properties…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate…
We shall give bounds on the spacing of zeros of certain functions belonging to the Laguerre-Polya class and satisfying a second order differential equation. As a corollary we establish new sharp inequalities on the extreme zeros of the…
Using the Laplace derivative a Perron type integral, the Laplace integral, is defined. Moreover, it is shown that this integral includes Perron integral and to show that the inclusion is proper, an example of a function is constructed,…
In this paper, we establish some new general Opial inequalities for Widder derivatives.
The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and…
It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. As applications, we obtain Gustavsson-Peetre interpolation of…
The goal of the paper is establishing the approximation of mixed partial derivatives of the second order of a function of several variables via modified Bernstein polynomials in the $L_1$ norm under the minimal regularity.
In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between…
Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.
The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs…