Open Mathematics，2023; 21: 20230157 https://doi.org/10.1515/math-2023-0157

Schur-power convexity of integral mean for convex functions on the co-ordinates

Huan-Nan Shi，Jing Zhang

Abstract: In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing onconvex functions on coordinate axes. Furthermore, we introduce novel and fascinating inequalities for binarymeans as a practical application.

Keywords: Schur-geometric convexity, Schur-harmonic convexity, monotonicity, Schur-power convexity,convex functions on the coordinates, inequality, binary means

MSC 2020: 26B25, 26D15, 26A51

10.1515_math-2023-0157.pdf