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Duality for Fractional Min-max Problems Involving Arcwise Connected and Generalized Arcwise Connected Functions

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Generalized Convexity and Generalized Monotonicity

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 502))

Abstract

In this paper, we introduce two duals for the fractional minmax pro gramming problem of the form:

$$ \begin{gathered} Minimize Maximize_{y \in Y\frac{{f(x,y)}} {{h(x,y)}}} \hfill \\ subject to g\left( x \right) \leqq 0, \hfill \\ \end{gathered} $$

subject to g(x) ≦ 0, and establish duality results under arcwise connectedness and generalized arcwise connectedness assumptions on the functions involved.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Deen Dayal Upadhyaya College, Shivaji Marg, Karampura, New Delhi, 110 015, India

    Pankaj Gupta

  2. Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110 007, India

    Davinder Bhatia

Authors
  1. Pankaj Gupta
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  2. Davinder Bhatia
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of the Aegean, 83200, Karlovassi/Samos, Greece

    Nicolas Hadjisavvas

  2. CODE and Department of Economics, Universitat Autonoma de Barcelona, 08193, Bellaterra, Spain

    Juan Enrique Martínez-Legaz

  3. Department of Mathematics Faculty of Sciences, Université de Pau, 64000, Pau, France

    Jean-Paul Penot

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© 2001 Springer-Verlag Berlin Heidelberg

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Gupta, P., Bhatia, D. (2001). Duality for Fractional Min-max Problems Involving Arcwise Connected and Generalized Arcwise Connected Functions. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-56645-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41806-1

  • Online ISBN: 978-3-642-56645-5

  • eBook Packages: Springer Book Archive

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