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We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…
Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H{\"o}lder…
In this paper, we introduce the higher order generalization of Bernstein type operators defined by (p,q)-integers. We establish some approximation results for these new operators by using the modulus of continuity.
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
In this article, we achieve some general statistical approximation results for $ \lambda $-Bernstein operators in addition to some other approximation properties. We prove a statistical Voronovskaja-type approximation theorem. We also…
We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under…
In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are…
We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of…
We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…
Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn…
We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…
We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…