![]()
AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
|
|||||||
The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name. |
|||||||
STUDIA MATHEMATICA - Issue no. 2 / 2011 | |||||||
Article: |
ON GRÜSS-TYPE INEQUALITIES FOR POSITIVE LINEAR OPERATORS. Authors: . |
||||||
Abstract: The classical form of Grüss’ inequality gives an estimate of the difference between the integral of the product and the product of the integrals of two functions in C[a, b]. It was first published by G. Grüss in [7]. The aim of this article is to discuss Grüss-type inequalities in C(X), the set of continuous functions defined on a compact metric space X. We consider a functional L(f) := H(f; x), where H : C(X) → C(X) is a positive linear operator and x Î X is fixed. Generalizing a result of Acu et al. [1], a quantitative Grüss-type inequality is obtained in terms of the least concave majorant of the classical modulus of continuity. The interest is in the degree of non-multiplicativity of the functional L. Moreover, for the case X = [a, b] we improve the inequality and apply it to various known operators, in particular those of Bernstein-, convolution- and Shepard-type. Mathematics Subject Classification (2010): 47A63, 41A25, 47B38. Keywords: Grüss-type inequality, compact metric space, least concave majorant of the modulus of continuity, convolution-type operator, Shepard interpolation operator. |
|||||||
![]() |
|||||||