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Čebyšev-Grüss-type inequalities revisited

In: Mathematica Slovaca, vol. 63, no. 5
Heiner Gonska - Ioan Raşa - Maria-Daniela Rusu

Details:

Year, pages: 2013, 1007 - 1024
Keywords:
Čebyšev inequality, Čebyšev-Grüss-type inequality, least concave majorant of the modulus of continuity, Hermite-Fejér interpolation operator, convolution-type operators, Gavrea's
About article:
We generalize and improve several inequalities of the Čebyšev-Grüss-type using least concave majorants of the moduli of continuity of the functions involved. Our focus is on normalized positive linear functionals. We discuss a problem posed by the two Gavreas and also give the solution of a stronger one. In a section about the non-multiplicativity of positive linear operators it is demonstrated that the previous use of second moments is not quite the right choice. This is documented in the case of the classical Hermite-Fejér and de La Vallée Poussin convolution operators.
How to cite:
ISO 690:
Gonska, H., Raşa, I., Rusu, M. 2013. Čebyšev-Grüss-type inequalities revisited. In Mathematica Slovaca, vol. 63, no.5, pp. 1007-1024. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0151-0

APA:
Gonska, H., Raşa, I., Rusu, M. (2013). Čebyšev-Grüss-type inequalities revisited. Mathematica Slovaca, 63(5), 1007-1024. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0151-0
About edition:
Published: 1. 10. 2013