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Strong \(n\)-convex \(n\)-normed spaces. (English) Zbl 1010.46024

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.

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.)
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