Pre-Grüss and Grüss-Ostrowski like inequalities in Banach spaces
Marek Niezgoda, Karol Gryszka · Mathematical Inequalities & Applications · 2022
For a given Banach space and its dual space we investigate a Chebyshev type functional. We derive a pre-Grss inequality for the functional. We discuss various variants of assumptions leading to this inequality. To do so, we employ some superquadratic as well as convex control functions in order to weaken the classical Dragomir's condition. Next, we establish a corresponding Grss-Ostrowski like inequalities for the space L p [a,b] .