On a minimax theorem of K. Fan

Construction of bipotentials and a minimax theorem of Fan

The bipotential theory is based on an extension of Fenchel’s inequality (see section 1 and example 1 in section 2). Despite several powerful applications (frictional contact [6], non-associated Drucker-Prager model [1], or Lemaitre plastic ductile damage law [2], to cite a few), the bipotentials don’t have yet a complete mathematical treatment. This is a second paper on the mathematics of the b...

A Zq-Fan theorem

In 1952, Ky Fan proved a combinatorial theorem generalizing the Borsuk-Ulam theorem stating that there is no Z2-equivariant map from the d-dimensional sphere S to the (d − 1)-dimensional sphere Sd−1. The aim of the present paper is to provide the same kind of combinatorial theorem for Dold's theorem, which is a generalization of the Borsuk-Ulam theorem when Z2 is replaced by Zq, and the spheres...

A Topological Minimax Theorem

We present a topological minimax theorem (Theorem 2.2). The topological assumptions on the spaces involved are somewhat weaker than those usually found in the literature. Even when reinterpreted in the convex setting of topological vector spaces, our theorem yields nonnegligible improvements, for example, of the Passy–Prisman theorem and consequently of the Sion theorem, contrary to most result...

Generalizations of the Fan-browder Fixed Point Theorem and Minimax Inequalities

In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained.

The fan theorem