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Minimax Theory and Applications pp 1–20Cite as

Nonlinear Two Functions Minimax Theorems

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 26))

Abstract

Let X and Y be nonempty sets. Let f, g : X × Y → ℝ be functions. Throughout this paper, we assume that f(x, y) ≤ g(x, y) for all (x, y) ∈ X × Y. A minimax theorem for f implies that, under certain conditions, the following equation holds:

$$ \mathop {\inf }\limits_Y \mathop {sup}\limits_X f(x,y) = \mathop {sup}\limits_X \mathop {\inf }\limits_Y f(x,y) $$
((*))

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Author information

Authors and Affiliations

  1. Department of Mathematics, Computer Institute, Beijing Polytechnic, Beijing, 100044, China

    Cao-Zong Cheng

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Bor-Luh Lin

Authors
  1. Cao-Zong Cheng
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  2. Bor-Luh Lin
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Catania, Catania, Italy

    Biagio Ricceri

  2. Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California, USA

    Stephen Simons

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© 1998 Springer Science+Business Media Dordrecht

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Cheng, CZ., Lin, BL. (1998). Nonlinear Two Functions Minimax Theorems. In: Ricceri, B., Simons, S. (eds) Minimax Theory and Applications. Nonconvex Optimization and Its Applications, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9113-3_1

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  • DOI: https://doi.org/10.1007/978-94-015-9113-3_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5030-4

  • Online ISBN: 978-94-015-9113-3

  • eBook Packages: Springer Book Archive

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