Abstract

A proper extension of Fan's minimax theorem, sharp in a sense, is provided. In particular, a natural kind of convexity for minimax inequalities arises. In addition a vector-valued Lax-Milgram theorem is derived, which in turn implies a characterization of the solvability of systems with infinitely many variational equations.

Author information

Contact details are reproduced from the original publication and may be historical.

M. Ruiz Galán

Dept. of Applied Mathematics, E.T.S. Ingeniería de Edificación, University of Granada, c/ Severo Ochoa s/n, 18071 Granada, Spain

mruizg@ugr.es

Keywords

  • Minimax theorems
  • Lax-Milgram theorem
  • variational equations

Mathematics Subject Classification

49K35, 49J40, 58E30

Suggested citation

M. Ruiz Galán. “An Intrinsic Notion of Convexity for Minimax.” Journal of Convex Analysis 21 (2014), No. 4, 1105–1139. https://doi.org/10.68381/jca21059

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.