Lp –Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

Quadrature Rules for Fuzzy Integrals

A unified generalization of some quadrature rules and error bounds

WENJUN LIU, YONG JIANG, AND ADNAN TUNA Abstract. By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson’s rules, but also give some new error bounds for other quadrature rules as special cases. Especially, two sharp error inequalities are derived when n is ...

Error bounds for interpolatory quadrature rules on the unit circle

For the construction of an interpolatory integration rule on the unit circle T with n nodes by means of the Laurent polynomials as basis functions for the approximation, we have at our disposal two nonnegative integers pn and qn, pn + qn = n − 1, which determine the subspace of basis functions. The quadrature rule will integrate correctly any function from this subspace. In this paper upper bou...

Inequalities between the Quadrature Operators and Error Bounds of Quadrature Rules

The order structure of the set of six operators connected with quadrature rules is established in the class of 3–convex functions. Convex combinations of these operators are studied and their error bounds for four times differentiable functions are given. In some cases they are obtained for less regular functions as in the classical results. Quadrature Rules, Inequalities and Error Bounds Szymo...

Lp BOUNDS FOR SINGULAR INTEGRALS AND MAXIMAL SINGULAR

Convolution type Calderr on-Zygmund singular integral operators with rough kernels p.v. (x)=jxj n are studied. A condition on implying that the corresponding singular integrals and maximal singular integrals map L p ! L p for 1 < p < 1 is obtained. This condition is shown to be diierent from the condition 2 H 1 (S n?1).