New cubature formulas and Hermite-Hadamard type inequalities using integrals over some hyperplanes in the \(d\)-dimensional hyper-rectangle

DOI10.1016/j.amc.2017.07.083zbMath1426.65035OpenAlexW2743238675MaRDI QIDQ1740159

Xianqiang Yang

Publication date: 29 April 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2017.07.083

zbMATH Keywords

cubatureerror estimatesapproximationbest constantscomponentwise convexity

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inequalities for sums, series and integrals (26D15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items (5)

On Hermite-Hadamard-Type Inequalities for Subharmonic Functions Over Circular Ring Domains ⋮ Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope ⋮ Certain quantum estimates on the parameterized integral inequalities and their applications ⋮ Extended Multidimensional Integration Formulas on Polytope Meshes ⋮ Hermite-Hadamard type inequalities for operator (p,h)-convex functions

Uses Software

• PolyMesher

Cites Work

• Unnamed Item
• Unnamed Item
• Approximations of differentiable convex functions on arbitrary convex polytopes
• Characterization of the existence of an enriched linear finite element approximation using biorthogonal systems
• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
• Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations
• A definiteness theory for cubature formulae of order two
• Gauss-Hermite interval quadrature rule
• The Midpoint Method of Numerical Integration
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• Centroidal Voronoi Tessellations: Applications and Algorithms
• Convexity results and sharp error estimates in approximate multivariate integration
• A simple necessary and sufficient condition for the enrichment of the Crouzeix-Raviart element
• Integration Formulae Based on the Trapezoidal Formula
• A version of Simpson's rule for multiple integrals

This page was built for publication: New cubature formulas and Hermite-Hadamard type inequalities using integrals over some hyperplanes in the \(d\)-dimensional hyper-rectangle