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Generalized Alomari Functionals

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012, Sibiu, Romania

    Ana-Maria Acu

  2. Faculty of Mathematics, University of Duisburg-Essen, Bismarckstr. 90, 47057, Duisburg, Germany

    Heiner Gonska

Authors
  1. Ana-Maria Acu
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  2. Heiner Gonska
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Correspondence to Ana-Maria Acu.

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Dedicated to professor Ioan Rasa on the occasion of his 65th birthday.

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Acu, AM., Gonska, H. Generalized Alomari Functionals. Mediterr. J. Math. 14, 1 (2017). https://doi.org/10.1007/s00009-016-0833-2

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  • DOI: https://doi.org/10.1007/s00009-016-0833-2

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