Some Remarks on Results Related to Ostrowski−Gruss Inequality

The article [14] published in 2007 titled “New bounds for the first inequality of Ostrowski−Gruss type and applications in numerical integration” contains very important results in the sense that the main idea of the article is unique, and it helps to generalize many established results. In the article [11], which appeared in the year 2013, we find exactly the same proving techniques used, leading to similar but slightly different results as compared to results stated in [14]. This arises the question: Why do two different authors, using exactly same proving techniques, arrive at different results? Now we compare results of the two articles and give some remarks on it and produce a better version.