| Peer-Reviewed

A Convex Hull’ Characterization

Received: 11 April 2014     Accepted: 7 May 2014     Published: 20 May 2014
Views:       Downloads:
Abstract

Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 2)
DOI 10.11648/j.pamj.20140302.13
Page(s) 40-48
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Convex, Linear, Game

References
[1] M.Carter Foundations of mathematical economics, Cambridge MIT PRESS, 2001.
[2] J.W.S. Cassels Measures of the non-convexity of sets and the Shapley-Folkman-Starr theorem Mathematical Proceedings of the Cambridge Philosophical Society Vol. 78 pp. 433-436, 1975.
[3] H.G. Egglestone Convexity Cambridge University press London, 1958.
[4] C.Faith Algebra I Rings, Modules, and Categories Springer-Verlag, 1981.
[5] F.Fineschi, R.Giannetti Adjoints of a Matrix Journal of Interdisciplinary Mathematics. Vol.11, No. 1, pp.39-65. Taru Publications, 2008 .
[6] J.B.Hiriart-Urruty, C.Lemaréchal Fundamentals of Convex Analysis Springer-Verlag, 2001.
[7] T. Iimura, T. Watanabe Existence of a pure strategy equilibrium in finite symmetric games where payoff functions are integrally concave Discrete Applied Mathematics, Forthcoming 2012.
[8] S. Karlin Mathematical Methods and Theory in Games, Programming, and Economics - The Theory of Infinite Games Addison-Wesley, 1959.
[9] Y. Wey A characterization and representation of the generalized inverse and its applicatations, Linear Algebra Appl. N. 280 pp 87-96, 1998.
[10] Lin Zhou A simple proof of the Shapley-Folkman theorem Economic Theory Vol.3, pp. 371-372, 1993.
Cite This Article
  • APA Style

    Franco Fineschi, Giovanni Quaranta. (2014). A Convex Hull’ Characterization. Pure and Applied Mathematics Journal, 3(2), 40-48. https://doi.org/10.11648/j.pamj.20140302.13

    Copy | Download

    ACS Style

    Franco Fineschi; Giovanni Quaranta. A Convex Hull’ Characterization. Pure Appl. Math. J. 2014, 3(2), 40-48. doi: 10.11648/j.pamj.20140302.13

    Copy | Download

    AMA Style

    Franco Fineschi, Giovanni Quaranta. A Convex Hull’ Characterization. Pure Appl Math J. 2014;3(2):40-48. doi: 10.11648/j.pamj.20140302.13

    Copy | Download

  • @article{10.11648/j.pamj.20140302.13,
      author = {Franco Fineschi and Giovanni Quaranta},
      title = {A Convex Hull’ Characterization},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {2},
      pages = {40-48},
      doi = {10.11648/j.pamj.20140302.13},
      url = {https://doi.org/10.11648/j.pamj.20140302.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140302.13},
      abstract = {Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - A Convex Hull’ Characterization
    AU  - Franco Fineschi
    AU  - Giovanni Quaranta
    Y1  - 2014/05/20
    PY  - 2014
    N1  - https://doi.org/10.11648/j.pamj.20140302.13
    DO  - 10.11648/j.pamj.20140302.13
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 40
    EP  - 48
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20140302.13
    AB  - Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.
    VL  - 3
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Department DISAG, University of Siena, Italy

  • Department DISAG, University of Siena, Italy

  • Sections