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Chebyshev-Grüss-type inequalities via discrete oscillations
Authors: Heiner Gonska, Ioan Raşa, Maria-Daniela Rusu
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Abstract
The classical form of Grüss' inequality, first published by G. Grüss in 1935, gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to introduce a new approach, presenting a new Chebyshev-Grüss-type inequality and applying to different well-known linear, not necessarily positive, operators. Some conjectures are presented. We also compare the new inequalities with some older results. In some cases this new approach gives better estimates than the ones already known.Heiner Gonska
University of Duisburg-Essen, Faculty of Mathematics,
Forsthausweg 2, 47057 Duisburg, Germany
E-mail: Ioan Raşa
Technical University of Cluj-Napoca, Department of
Mathematics, Str. C. Daicoviciu, 15, RO-400020
Cluj-Napoca, România
E-mail: Maria-Daniela Rusu
University of Duisburg-Essen, Faculty of Mathematics,
Forsthausweg 2, 47057 Duisburg, Germany
E-mail:
University of Duisburg-Essen, Faculty of Mathematics,
Forsthausweg 2, 47057 Duisburg, Germany
E-mail: Ioan Raşa
Technical University of Cluj-Napoca, Department of
Mathematics, Str. C. Daicoviciu, 15, RO-400020
Cluj-Napoca, România
E-mail: Maria-Daniela Rusu
University of Duisburg-Essen, Faculty of Mathematics,
Forsthausweg 2, 47057 Duisburg, Germany
E-mail:
Fulltext
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