Malčeski, Risto Strong \(n\)-convex \(n\)-normed spaces. (English) Zbl 1010.46024 Mat. Bilt. 21, No. 47, 81-102 (1997). The author treats \(n\)-normed spaces in the sense of A. Misiak [Math. Nachr. 140, 299-319 (1989; Zbl 0673.46012)]. He defines a property which he calls strong \(n\)-convexity for such spaces, generalizing the notion of strictly 2-convex 2-normed spaces considered in [C. Diminnie, S. Gähler and A. White, Math. Nachr. 88, 363-372 (1979; Zbl 0417.46022)], and derives some properties of such spaces. Reviewer: Zoran Kadelburg (Beograd) Cited in 9 Documents MSC: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.) 46B99 Normed linear spaces and Banach spaces; Banach lattices 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) Keywords:\(n\)-inner product; \(n\)-pre-Hilbert space; \(n\)-linear mapping; \(n\)-norm middle point Citations:Zbl 0673.46012; Zbl 0417.46022 PDFBibTeX XMLCite \textit{R. Malčeski}, Mat. Bilt. 21, 81--102 (1997; Zbl 1010.46024)