Continuous refinements of some Jensen-type inequalities via strong convexity with applications-Reference-Cited by-同舟云学术

Continuous refinements of some Jensen-type inequalities via strong convexity with applications

Published:2022-05-23 Issue:1 Volume:2022 Page:
ISSN:1029-242X
Container-title:Journal of Inequalities and Applications
language:en
Short-container-title:J Inequal Appl

Author:

Nikolova Ludmila,Persson Lars-Erik,Varošanec Sanja^ORCID

Abstract

AbstractIn this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite–Hadamard, Hölder, and Popoviciu type inequalities. As particular cases we point out the corresponding results for sums and integrals showing that our results contain both several well-known but also some new results for these special cases.

Funder

University of Zagreb, Faculty of Science

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Link

https://link.springer.com/content/pdf/10.1186/s13660-022-02801-4.pdf

Reference21 articles.

1. Abramovich, S., Jameson, G., Sinnamon, G.: Refining of Jensen’s inequality. Bull. Math. Soc. Sci. Math. Roum. 47, 3–14 (2004)

2. Abramovich, S., Persson, L.E.: Fejer and Hermite-Hadamard type inequalities for quasiconvex functions. Math. Notes Acad. Sci. 102(5–6), 599–609 (2017)

3. Abramovich, S., Persson, L.E.: Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity. Math. Inequal. Appl. 23(2), 447–458 (2020)

4. Azócar, A., Nikodem, K., Roa, G.: Fejér-type inequalities for strongly convex functions. Ann. Math. Sil. 26, 43–54 (2012)

5. Dragomir, S.S., Khan, M.A., Abathun, A.: Refinement of the Jensen integral inequality. Open Math. J. 14, 221–228 (2016)

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