Abstract
The purpose of this paper is to establish a weighted Montgomery identity for k points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for k points. For k=2, we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.
Highlights
In 1938, Ostrowski [1] proved the following inequality which approximates a function by its integral average.Theorem 1
Since the introduction of this theory, it became a point of research to extend known classical differential and integral results to time scales
We briefly introduce the theory of time scales
Summary
In 1938, Ostrowski [1] proved the following inequality which approximates a function by its integral average. Since the introduction of this theory, it became a point of research to extend known classical differential and integral results to time scales. Following this line of thought, Bohner and Matthews [4] extended Theorem 1 to time scales by proving the following result. H2 (x, b)) , Abstract and Applied Analysis where h2(⋅, ⋅) is given in Definition 12 and M = supa
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