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  • 1990-1994  (1)
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    Electronic Resource
    Electronic Resource
    Regular hexagons in normed spaces and a theorem of Walter Benz (1993)
    Springer
    Aequationes mathematicae 45 (1993), S. 163-166 
    Details
    ISSN: 1420-8903
    Keywords: 46B20 ; 39B52 ; 51A10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new proof is given for the following recent result of W. Benz [1]. Suppose thatG: E → E, whereE is a real normed vector space of dimension at least 3, is such that, for somep o 〉 0, $$G(x + h) - G(x)\,and h\,\,are linearly dependent whenever\,\,\left\| h \right\| = p_0 .$$ Then there existx o ∈ E andq o ∈ ℝ such thatG(x) = q 0x + x0 for allx ∈ E. The new proof is based on existence theorems for regular hexagons in normed spaces which may be of some interest in themselves. Hexagons are also helpful in deducing similar results for certain two-dimensional spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01855875
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