Abstract
Here we present weighted fractional Iyengar type inequalities with respect to L p norms, with 1 ≤ p ≤ ∞ . Our employed fractional calculus is of Caputo type defined with respect to another function. Our results provide quantitative estimates for the approximation of the Lebesgue–Stieljes integral of a function, based on its values over a finite set of points including at the endpoints of its interval of definition. Our method relies on the right and left generalized fractional Taylor’s formulae. The iterated generalized fractional derivatives case is also studied. We give applications at the end.
Highlights
We are motivated by the following famous Iyengar inequality (1938), [1]
We present the following Caputo type generalized g-fractional Iyengar type inequality: (20)
We could give many other interesting applications that are based in our other theorems, due to lack of space we skip this task
Summary
/ N, by [3], pp. 360–361, we have that Daα+;g f ∈ C ([ a, b])
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