Generalized Alomari Functionals
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A generalized form of certain integral inequalities investigated by Guessab, Schmeisser and Alomari is given. The trapezoidal, midpoint, Simpson, Newton–Simpson rules are obtained as special cases. Also, inequalities for the generalized Alomari functional in terms of n-th order moduli are given and applied to some known quadrature rules.
Keywords(Four point) quadrature formula K-functional modulus of continuity
Mathematics Subject Classification41A44 41A55 41A80 65D30 41A80 65D30
The project was financed from Lucian Blaga University of Sibiu research Grants LBUS-IRG-2016-02. It was carried out while the second author was visiting LBUS under an Erasmus \(+\) grant. We are grateful to the reviewer for the detailed valuable comments and for the proposed corrections which improve our manuscript.
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