Related papers: Weighted Orthogonal Polynomials-Based Generalizati…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
In this article, we introduce and study accelerated Landweber methods for linear ill-posed problems obtained by an alteration of the coefficients in the three-term recurrence relation of the \nu-methods. The residual polynomials of the…
For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted $L^p$ space is given. The result is then used to…
This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…
In this paper, we establish a generalized H{\"o}lder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabilization of some damped wave-like evolution equations. This…
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
In this paper, we establish some new general Opial inequalities for Widder derivatives.
We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses…
Starting with some fundamental concepts, in this article we present the essential aspects of spectral methods and their applications to the numerical solution of Partial Differential Equations (PDEs). We start by using Lagrange and…
In this article we derive some polynomial inequalities for Mertens functions.
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
In this paper we obtain some properties of orthogonal polynomials given by a weight function which is a limit density of a rescaled discrete-time quantum walk on the line.
We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving differential operators is employed. Generalized Wilson…
The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone…
We prove generalized weighted Ostrowski and Ostrowski--Gr\"uss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…