Geodesic
Some Grüss Type Inequalities for Fréchet Differentiable Mappings
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 571

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $X$ be a Hilbert $C^{*}$-module on $C^{*}$-algebra $A$ and $p\in A$. We denote by $D_{p}(A ,X)$ the set of all continuous functions $f : A \rightarrow X$, which are Fréchet differentiable on a open neighborhood $U$ of $p$. Then, we introduce some generalized semi-inner products on $D_{p}(A ,X)$, and using them some Grüss type inequalities in semi-inner product $C^*$-module $D_{p}(A ,X)$ and $D_{p}(A ,X^n)$ are established.
Classification : 26D10 46C05, 46L08
Keywords: Fréchet differentiable mappings, $C^*$-modules, Grüss inequality 
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     author = {T. Teimouri-Azadbakht and A. G Ghazanfari},
     title = {Some {Gr\"uss} {Type} {Inequalities} for {Fr\'echet} {Differentiable} {Mappings}},
     journal = {Kragujevac Journal of Mathematics},
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T. Teimouri-Azadbakht; A. G Ghazanfari. Some Grüss Type Inequalities for Fréchet Differentiable Mappings. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 571 . http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a7/