Grüss' inequality for positive linear functionals

Andrica, Dorin; Badea, Cătălin

doi:10.1007/bf01848061

Cited by 47 publications

(17 citation statements)

References 11 publications

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our present work is to a large extent motivated by a theorem that can be found in the paper [2] by Andrica and Badea. Here we cite a special form of it.…”

Section: Introductionmentioning

confidence: 96%

Grüss-type and Ostrowski-type inequalities in approximation theory

2011

View full text Add to dashboard Cite

We discuss the Grüss inequalities on spaces of continuous functions defined on a compact metric space. Using the least concave majorant of the modulus of continuity, we obtain the Grüss inequality for the functional L.f / D H.f I x/; where H W C OEa; b ! C OEa; b is a positive linear operator and x 2 OEa; b is fixed. We apply this inequality in the case of known operators, e.g., the Bernstein operator, the HermiteFejér interpolation operator, and convolution-type operators. Moreover, we deduce Grüss-type inequalities using the Cauchy mean-value theorem, thus generalizing results of Chebyshev and Ostrowski. The Grüss inequality on a compact metric space for more than two functions is given, and an analogous Ostrowski-type inequality is obtained. The latter, in turn, leads to one further version of the Grüss inequality. In the appendix, we prove a new result concerning the absolute first-order moments of the classic Hermite-Fejér operator.

show abstract

“…Our present work is to a large extent motivated by a theorem that can be found in the paper [2] by Andrica and Badea. Here we cite a special form of it.…”

Section: Introductionmentioning

confidence: 96%

Grüss-type and Ostrowski-type inequalities in approximation theory

2011

View full text Add to dashboard Cite

show abstract

“…We also need to recall, for the first section, the definition of isotonic linear functional. This definition can be also find in papers as [2], [3], [8], [12] and the references therein. Definition 1.…”

Section: Introductionmentioning

confidence: 99%

Several applications for a local Young-type inequality

Ciurdariu¹

2019

ijma

View full text Add to dashboard Cite

show abstract

“…Thus, they provide, for example, Jessen's inequality, which is a functional form of Jensen's inequality (see [2], [15] and [16]). For other inequalities for isotonic functionals see [1], [4]- [14] and [17]- [20].…”

Section: Introductionmentioning

confidence: 99%