Shih, Mauhsiang; Tan, Kokkeong A further generalization of Ky Fan’s minimax inequality and its applications. (English) Zbl 0554.49005 Stud. Math. 78, 279-287 (1984). This paper generalizes the well-known Ky Fan minimax inequality to non- compact convex sets in a Hausdorff topological vector space and to a pair of functions. The proof is based on the Brézis-Nirenberg-Stampacchia lemma about the non-empty intersection of all values of some KKM multi- valued map. By using this generalization of Ky Fan’s inequality a Dugundji-Granas variational inequality is generalized to set-valued maps and to non-compact sets in Hausdorff space. As a consequence two new fixed point theorems for pseudo-contractive and for nonexpansive maps in Hilbert space are proved. Reviewer: Z.Wyderka Cited in 5 Documents MSC: 49J35 Existence of solutions for minimax problems 47H10 Fixed-point theorems 49J40 Variational inequalities 54C60 Set-valued maps in general topology 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.) 52A07 Convex sets in topological vector spaces (aspects of convex geometry) 52A40 Inequalities and extremum problems involving convexity in convex geometry 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:Ky Fan minimax inequality; non-compact convex sets; KKM multi-valued map; Dugundji-Granas variational inequality; Hausdorff space PDFBibTeX XMLCite \textit{M. Shih} and \textit{K. Tan}, Stud. Math. 78, 279--287 (1984; Zbl 0554.49005) Full Text: DOI EuDML