Cubature Error Bounds for Analytic Functions

Error Estimates for Polyharmonic Cubature Formulas

In the present article we shall present basic features of a polyharmonic cubature formula of degree s and corresponding error estimates. Main results are Markov-type error estimates for differentiable functions and error estimates for functions f which possess an analytic extension to a sufficiently large ball in the complex space Cd . 2000 AMS subject classification: 65D30, 32A35

On the Smolyak cubature error for analytic functions

Coefficient Bounds for Analytic bi-Bazileviv{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers

In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers.  Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

The Role of Frolov's Cubature Formula for Functions with Bounded Mixed Derivative

We prove upper bounds on the order of convergence of Frolov’s cubature formula for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study worst-case integration errors for Besov Bp,θ and Triebel-Lizorkin spaces F s p,θ and our results treat the whole range of admissible parameters (s ≥ 1/p). In parti...