Some Grüss Type Inequalities for Fréchet Differentiable Mappings
Download PDF
Authors: T. TEIMOURI-AZADBAKHT AND A. G GHAZANFARI
DOI: 10.46793/KgJMat2004.571T
Abstract:
Let X be a Hilbert C∗-module on C∗-algebra A and p ∈ A. We denote by Dp(A,X) the set of all continuous functions f : A → X, which are Fréchet differentiable on a open neighborhood U of p. Then, we introduce some generalized semi-inner products on Dp(A,X), and using them some Grüss type inequalities in semi-inner product C∗-module Dp(A,X) and Dp(A,Xn) are established.
Keywords:
Fréchet differentiable mappings, C∗-modules, Grüss inequality.
References:
[1] S. S. Dragomir, Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers Inc., New York, 2005.
[2] S. S. Dragomir, A Grüss type discrete inequality in inner product spaces and applications, J. Math. Anal. Appl. 250 (2000), 494–511.
[3] A. G. Ghazanfari and S. S. Dragomir, Bessel and Grüss type inequalities in inner product modules over Banach ∗-algebra, Linear Algebra Appl. 434 (2011), 944–956.
[4] G. Grüss, Über das Maximum des absoluten Betrages von 
∫ abf(x)g(x)dx − 
∫ abf(x)dx∫ abg(x)dx, Math. Z. 39(1934), 215–226.
[5] D. Ilišević and S. Varošanec, Grüss type inequalities in inner Product modules, Proc. Amer. Math. Soc. 133 (2005), 3271–3280.
[6] A. I. Kechriniotis and K. K. Delibasis, On generalizations of Grüss inequality in inner product spaces and applications, J. Inequal. Appl. 2010 (2010), Article ID 167091, 18 pages.
[7] E. C. Lance, Hilbert C∗-Modules, London Math. Soc. Lecture Note Ser. 210, Cambridge University Press, 1995.
[8] X. Li, R. N. Mohapatra and R. S. Rodriguez, Grüss-type inequalities, J. Math. Anal. Appl. 267(2) (2002), 434–443.
[9] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, 1993.
Login:
