N. Ziane, M. Ait Mansour, J. Lahrache, Some fixed point results via a minimax approach

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DOI: 10.23952/asvao.8.2026.1.07

Volume 8, Issue 1, 1 April 2026, Pages 113-125

Abstract. In this paper, we investigate a finite dimensional case of Ricceri’s question [given a real normed space $E$ , a closed, convex, and unbounded set $X\subseteq E$ , and a function $f:X\to X$ , find suitable conditions under which, for each $y\in X$ , the function defined by $x\to J(x,y):=\|x-f(x)\|-\|y-f(x)\|$ has at most one global minimum in $X$ ] by providing several general and numerical examples of a such function $f$ . We observe that other alternatives on the choice of the functional $J$ defined above could lead to new fixed point theorems from Ricceri’s minimax approach.

How to Cite this Article:
N. Ziane, M. Ait Mansour, J. Lahrache, Some fixed point results via a minimax approach, Appl. Set-Valued Anal. Optim. 8 (2026), 113-125.