Journal of Convex Analysis 26 (2019), No. 2, 437--448
Copyright Heldermann Verlag 2019
On Inequalities for Convex Functions
Luis Bernal-González
Dep. de Análisis Matemático, Universidad de Sevilla, Avenida Reina Mercedes, Sevilla 41080, Spain
lbernal@us.es
Pablo Jiménez-Rodríguez
Dept. of Mathematical Sciences, Kent State University, Summit Street, Kent, OH 44242, U.S.A.
pjimene1@kent.edu
Gustavo A. Munoz-Fernández
Dep. de Análisis y Matemática Aplicada, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid 28040, Spain
gustavo_fernandez@mat.ucm.es
Juan B. Seoane-Sepúlveda
Dep. de Análisis y Matemática Aplicada, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid 28040, Spain
jseoane@ucm.es
We study some properties enjoyed by convex functions. Among other results, we show some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the particular case where three aligned points are considered in a normed space.
Keywords: Convex function, convexity, midconvexity, inequality.
MSC: 26A51, 26B25, 39B62
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