Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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. Muñoz-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

Keywords

  • Convex function
  • convexity
  • midconvexity
  • inequality

Mathematics Subject Classification

26A51, 26B25, 39B62

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Suggested citation

L. Bernal-González, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. “On Inequalities for Convex Functions.” Journal of Convex Analysis 26 (2019), No. 2, 437–448. https://doi.org/10.68381/jca26022

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press.