Khan, Muhammad Adil; Khan, Shahid; Ullah, Inam; Khan, Khuram Ali; Chu, Yu-Ming A novel approach to the Jensen gap through Taylor’s theorem. (English) Zbl 1472.26009 Math. Methods Appl. Sci. 44, No. 5, 3324-3333 (2021). Summary: This article presents a new bound for the Jensen gap in classical as well as in generalized form through an integral identity deduced from Taylor’s theorem. A discussion on the accuracy of the classical bound, through a numerical experiment, is a part of the paper. Also, the proposed bounds generate a bound for the Hermite-Hadamard gap and some reverses of the Hölder inequality. Finally, the paper deals with estimations of the Csiszár divergence and of some of its special cases. Cited in 6 Documents MSC: 26D15 Inequalities for sums, series and integrals 26A51 Convexity of real functions in one variable, generalizations 94A17 Measures of information, entropy Keywords:convex function; Csiszár divergence; Hermite-Hadamard inequality; Hölder inequality; Jensen inequality; Taylor’s theorem PDFBibTeX XMLCite \textit{M. A. Khan} et al., Math. Methods Appl. Sci. 44, No. 5, 3324--3333 (2021; Zbl 1472.26009) Full Text: DOI