This article is cited in 11 papers

Research articles

Chebyshev–Grüss-type inequalities via discrete oscillations

Heiner Gonska^a, Ioan Raşa^b, Maria-Daniela Rusu<sup>a

a</sup> University of Duisburg-Essen, Faculty of Mathematics, Forsthausweg 2, 47057 Duisburg, Germany
^b Technical University of Cluj-Napoca, Department of Mathematics, Str. C. Daicoviciu, 15, RO-400020 Cluj-Napoca, Romania

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.

Keywords and phrases: Chebyshev–Grüss-type inequalities, least concave majorant of the modulus of continuity, oscillations, Lagrange operator, Bernstein operator, King-type operators, $S_{\Delta_n}$ operator, Bleimann–Butzer–Hahn operator, Baskakov operator, Mirakjan–Favard–Szász operator.

MSC: 26D10, 26D15, 41A25, 47A58

Received: 15.07.2013

Language: English