Injectiveness and Discontinuity of Multiplicative Convex Functions

Pablo Jiménez-Rodríguez, María E. Martínez-Gómez, Gustavo A. Muñoz-Fernández and Juan B. Seoane-Sepúlveda
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Pablo Jiménez-Rodríguez: Departamento de Matemática Aplicada, Campus Duques de Soria, Universidad de Valladolid, 42004 Soria, Spain
María E. Martínez-Gómez: Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
Gustavo A. Muñoz-Fernández: Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), Plaza de Ciencias 3, Universidad Complutense de Madrid, 28040 Madrid, Spain
Juan B. Seoane-Sepúlveda: Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), Plaza de Ciencias 3, Universidad Complutense de Madrid, 28040 Madrid, Spain

Mathematics, 2021, vol. 9, issue 9, 1-15

Abstract: In the present work we study the set of multiplicative convex functions. In particular, we focus on the properties of injectiveness and discontinuity. We will show that a non constant multiplicative convex function is at most 2-injective, and construct multiplicative convex functions which are discontinuous at infinitely many points.

Keywords: convexity; convex function; multiplicative convex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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