Čebyšev-Grüss-type inequalities revisited-Reference-Cited by-同舟云学术

Čebyšev-Grüss-type inequalities revisited

Published:2013-10-01 Issue:5 Volume:63 Page:1007-1024
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Gonska Heiner¹,Raşa Ioan²,Rusu Maria-Daniela¹

Affiliation:

1. Faculty of Mathematics, University of Duisburg-Essen, Forsthausweg 2, D-47057, Duisburg, Germany

2. Department of Mathematics, Technical University, Str. C. Daicoviciu, 15, RO-400020, Cluj-Napoca, Romania

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.2478/s12175-013-0151-0.pdf

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