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Hadamard Majorants for the Convex Order and Applications

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Combining Soft Computing and Statistical Methods in Data Analysis

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

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Abstract

The problem of establishing Hadamard-type inequalities for convex functions on d-dimensional convex bodies (d ≥ 2) translates into the problem of finding appropriate majorants of the involved random vector for the usual convex order. In this work, we use a stochastic approach based on the Brownian motion to establish a multidimensional version of the classical Hadamard inequality. The main result is closely related to the Dirichlet problem and is applied to obtain inequalities for harmonic functions on general convex bodies.

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Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística e Investigación Operativa, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain

    Jesús de la Cal

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Javier Cárcamo

  3. Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain

    Luis Escauriaza

Authors
  1. Jesús de la Cal
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  2. Javier Cárcamo
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  3. Luis Escauriaza
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Editor information

Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

  4. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  5. Systems Research Institute, Polish Academy of Science, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hryniewicz

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de la Cal, J., Cárcamo, J., Escauriaza, L. (2010). Hadamard Majorants for the Convex Order and Applications. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_19

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

  • eBook Packages: EngineeringEngineering (R0)

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