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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.48 no.2 Bogotá July/Dec. 2014 


Multiplicative Relaxation with respect to Thompson's Metric

Relajamiento multiplicativo con respecto a la métrica de Thompson


1Karlsruhe Institute of Technology, Karlsruhe, Germany. Email:


We give a condition so that certain mixed monotone mappings on function spaces have a contractive multiplicative relaxation with respect to Thompson's metric. The corresponding fixed point theorem can be applied to special types of integral equations, for example.

Key words: Thompson metric, Mixed monotone mappings, Fixed points, Contraction, Relaxation.

2000 Mathematics Subject Classification: 47H10, 47H07.


Damos una condición para que ciertas aplicaciones monótonas mixtas sobre espacios de funciones tengan una relajación multiplicativa con respecto a las métricas de Thompson. El correspondiente teorema de punto fijo puede ser aplicado a tipos especiales de ecuaciones integrales, por ejemplo.

Palabras clave: Metrica de Thompson, aplicación mixta monotona, puntos fijos, contracción, relajación.

Texto completo disponible en PDF


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[6] D. H. Hyers, G. Isac, and T. M. Rassias, Topics in Nonlinear Analysis and Applications, World Scientific,         [ Links ] 1997.

[7] M. D. Rus, The Method of Monotone Iterations for Mixed Monotone Operators, Ph.D. Thesis Summary, Babes-Bolyai University, Romania,         [ Links ] 2010.

[8] A. Thompson, 'On Certain Contraction Mappings in a Partially Ordered Vector Space', Proc. Am. Math. Soc. 14, (1963), 438-443.         [ Links ]

(Recibido en febrero de 2014. Aceptado en agosto de 2014)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

    AUTHOR  = {Herzog, Gerd},
    TITLE   = {{Multiplicative Relaxation with respect to Thompson's Metric}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2014},
    volume  = {48},
    number  = {2},
    pages   = {211--217}