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Research Article | Open Access

A refinement of Jensen's inequality through abstract convexity

Ramazan Tinaztepe1, Gultekin Tinaztepe2( )
Department of Mathematics and Computer Science, College of Science and General Studies, Alfaisal University, P.O. Box 50927, 11533 Riyadh, Saudi Arabia
Akdeniz University, Vocational School of Technical Sciences, Dumlupınar Bulvarı, Antalya 07058, Turkey
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Abstract

In this study, the Jensen inequality has been refined. To achieve this, we employ the fact that an abstract convex function with certain structural properties can be bounded from below in a neighborhood of its global minimum in terms of the norm of its gradient. Some examples have been provided to show the extent of refinement.

Keywords

Jensen inequalityabstract convexityrefinementoptimization
CLC number: 26A51, 26D07, 26D15

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AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 7543-7554
DOI: 10.3934/math.2026309

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Cite this article:
Tinaztepe R, Tinaztepe G. A refinement of Jensen's inequality through abstract convexity. AIMS Mathematics, 2026, 11(3): 7543-7554. https://doi.org/10.3934/math.2026309

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Received: 17 December 2025
Revised: 01 March 2026
Accepted: 09 March 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)