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

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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 
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/
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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},
     pages = {571 },
     year = {2020},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a7/}
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