Abstract

Multiplicative convex functions have been mimicking the behavior of convex functions, but focusing on geometric average, instead of arithmetic average. In the present note we propose a different definition which focuses on the arithmetic operations taking part and we study the resulting functions. A characterization is also provided.

Author information

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

Pablo Jiménez-Rodríguez

Dept. of Mathematical Sciences, Kent State University, Kent, OH 44242, U.S.A.

pjimene1@kent.edu

Maria E. Martínez-Gómez

Dep. de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

mariae24@ucm.es

Gustavo A. Muñoz-Fernández

Dep. de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

gustavo_fernandez@mat.ucm.es

Juan B. Seoane-Sepúlveda

Dep. de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

jseoane@ucm.es

Keywords

  • Convexity
  • convex function
  • multiplicative convex

Mathematics Subject Classification

26A51, 30C45

Suggested citation

P. Jiménez-Rodríguez, M. E. Martínez-Gómez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. “Describing Multiplicative Convex Functions.” Journal of Convex Analysis 27 (2020), No. 3, 935–942. https://doi.org/10.68381/jca27047

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press.