Related papers: Direct and inverse theorems for Bernstein operator…
We extend the classical Bernstein inequality to a general setting including Schr{\"o}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreover , we prove a new reverse inequality that can be seen…
The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…
We study power series of members of a class of positive linear operators reproducing linear function and constituting a link between genuine Bernstein-Durrmeyer and classical Bernstein operators. Using the eigenstructure of the operators we…
In this paper, we describe two novel changes to the Baskakov-Durrmeyer operators that improve their approximation performance. These improvements are especially designed to produce higher rates of convergence, with orders of one or two.…
A new Goodman-Sharma modification of the Baskakov operator is presented for approximation of bounded and continuous on $[0,\,\infty)$ functions. In our study on the approximation error of the proposed operator we prove direct and strong…
In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear…
We obtain matching direct and inverse theorems for the degree of weighted $L_p$-approximation by polynomials with the Jacobi weights $(1-x)^\alpha (1+x)^\beta$. Combined, the estimates yield a constructive characterization of various…
In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual…
We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.
The main aim of this paper is to show that the nonlinear Choquet integral can be used to construct nonlinear approximation operators, exactly as by the use in probability of the Lebesgue-type integral, linear and positive approximation…
In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and…
We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.
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…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
This paper offers a newly created integral approach for operators employing the orthogonal modified Laguerre polynomials and P\u{a}lt\u{a}nea basis. These operators approximate the functions over the interval $[0,\infty)$. Further, the…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…
In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally,…
In this work, a connection between some spectral properties of direct sum of operators in the direct sum of Hilbert spaces and its coordinate operators has been investigated.