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Journal of Convex Analysis 28 (2021), No. 1, 001--010
Copyright Heldermann Verlag 2021

A Majorization Gradient Inequality for Symmetric Convex Functions

Marek Niezgoda
Department of Applied Mathematics and Computer Science, University of Life Sciences, 20-950 Lublin, Poland

We extend the standard two-points gradient inequality for a differentiable convex function to a four-points version satisfying Sherman's majorization condition.

Keywords: Convex function, gradient inequality, majorization, doubly stochastic matrix, Sherman's inequality.

MSC: 26B25, 26D10, 52A41.

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