Generalized Alomari functionals
Ana Maria Acu, Heiner Gonska

TL;DR
This paper introduces a generalized Alomari functional that unifies various classical integral inequalities and quadrature rules, providing new bounds and applications for numerical integration.
Contribution
It extends existing inequalities to a generalized functional framework, encompassing trapezoidal, midpoint, Simpson, and Newton-Simpson rules as special cases.
Findings
Derived inequalities for the generalized Alomari functional using the n-th order modulus.
Established bounds for classical quadrature rules within the generalized framework.
Applied the inequalities to improve error estimates in numerical integration.
Abstract
We consider a generalized form of certain integral inequalities given by Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson, Newton-Simpson rules are obtained as special cases. Also, inequalities for the generalized Alomari functional in terms of the -th order modulus, , are given and applied to some known quadrature rules.
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