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Injectiveness and Discontinuity of Multiplicative Convex Functions

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  • Pablo Jiménez-Rodríguez

    (Departamento de Matemática Aplicada, Campus Duques de Soria, Universidad de Valladolid, 42004 Soria, Spain
    All authors contributed equally to this work.)

  • 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
    All authors contributed equally to this work.)

  • 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
    All authors contributed equally to this work.)

  • 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
    All authors contributed equally to this work.)

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.

Suggested Citation

  • Pablo Jiménez-Rodríguez & María E. Martínez-Gómez & Gustavo A. Muñoz-Fernández & Juan B. Seoane-Sepúlveda, 2021. "Injectiveness and Discontinuity of Multiplicative Convex Functions," Mathematics, MDPI, vol. 9(9), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1035-:d:548304
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