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.
Citation: Ramazan Tinaztepe, Gultekin Tinaztepe. A refinement of Jensen's inequality through abstract convexity[J]. AIMS Mathematics, 2026, 11(3): 7543-7554. doi: 10.3934/math.2026309
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.
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Ramazan Tinaztepe, Gultekin Tinaztepe. A refinement of Jensen's inequality through abstract convexity[J]. AIMS Mathematics, 2026, 11(3): 7543-7554. doi: 10.3934/math.2026309
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