New refinement of the Jensen inequality associated to certain functions with applications

Author:

Adil Khan Muhammad,Pečarić Ðilda,Pečarić Josip

Abstract

AbstractThis article proposes a new refinement of the celebrated Jensen inequality. Some refinements have been obtained for quasi-arithmetic means, Hölder and Hermite–Hadamard inequalities. Several applications are given in information theory. A more general refinement of Jensen inequality is presented associated to n functions.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference22 articles.

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2. Adil Khan, M., Pečarić, Ð., Pečarić, J.: On Zipf–Mandelbrot entropy. J. Comput. Appl. Math. 346, 192–204 (2019)

3. Adil Khan, M., Pečarić, Ð., Pečarić, J.: Bounds for Shannon and Zipf–Mandelbrot entropies. Math. Methods Appl. Sci. 40(18), 7316–7322 (2017)

4. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc., Ser. B 39, 1–38 (1977)

5. Adil Khan, M., Hanif, M., Khan, Z.A., Ahmad, K., Chu, Y.-M.: Association of Jensen inequality for s-convex function. J. Inequal. Appl. 2019, Article ID 162 (2019)

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