Related papers: Approximation by complex Szasz-Durrmeyer-Chlodowsk…

This paper studies a class of multivariate Kantorovich-kernel neural network operators, including the deep Kantorovich-type neural network operators studied by Sharma and Singh. We prove density results, establish quantitative convergence…

We prove some general Sobolev-Orlicz, Nash and Faber-Krahn inequalities for positive operators of given ultracontractive norms of the spectral projectors on ]0, lambda]. For invariant operators on coverings of finite simplicial complexes…

In the Orlicz type spaces ${\mathcal S}_{M}$, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of…

In this paper, First we have given the modified form of (p,q)-analogues of Bernstein and Bernstein operators [21-23] and then we introduce a new analogue of Bernstein-Kantorovich operators which we call as (p,q)-Bernstein-Kantorovich…

In this work, wavelet-based filtering operators are constructed by introducing a basic function $D(t_1, t_2, t_3)$ using a general wavelet transform. The cardinal orthogonal scaling functions (COSF) provide an idea to derive the standard…

We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently by Levitin and Shargorodsky, [math.SP/0212087]. We find…

In this paper, we study the almost everywhere convergence results of Schr\"odinger operator with complex time along curves. We also consider the fractional cases. All results are sharp up to the endpoints.

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…

We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka--\L ojaziewicz (KL) inequality we establish new convergence rates…

We introduce a proximal limited--memory quasi--Newton scheme for minimizing the sum of a continuously differentiable function and a proper, lower semicontinuous and prox-bounded, possibly nonsmooth, function. Both functions might be…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…

We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic dependence on the parameters as considered in [Cl.~Schillings…

In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces,…

In this paper, we investigate Durrmeyer-type generalizations of maximum-minimum neural network operators. The primary objective of this study is to establish the convergence of these operators in the $L^{p}$ norm for functions $f\in…

Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in…

In this paper, we introduce a new sequence of operators based on the Gr\"unwald interpolation operators on Chebyshev nodes on the space $L^p[0,{\pi}]$. The operators we consider are integral variants of the Gr\"unwald interpolation…

In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…

In this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of continuity in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative…

Approximation properties of multivariate Kantorovich-Kotelnikov type operators generated by different band-limited functions are studied. In particular, a wide class of functions with discontinuous Fourier transform is considered. The…

In the present paper we establish sharp exponential decay estimates for operator and integral kernels of the (not necessarily self-adjoint) operators $L=-(\nabla-i\mathbf{a})^TA(\nabla-i\mathbf{a})+V$. The latter class includes, in…