Banach-Mazur distance between convex quadrangles

• Autorzy: Lassak M.
• Języki publikacji: EN

Abstrakty

EN

It is proved that the Banach–Mazur distance between arbitrary two convex quadrangles is at most 2. The distance equals 2 if and only if the pair of these quadrangles is a parallelogram and a triangle.

Słowa kluczowe

EN

Banach-Mazur distance; convex body; convex quadrangle; parallelogram; triangle

PL

odległość Banacha-Mazura; bryła wypukła; czwotokąt wypukły; równoległobok; trójkąt

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 4
• Strony: 989--993
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Lassak M.

• Institute of Mathematics and Physics, University of Technology and Life Sciences, 85-789 Bydgoszcz, Poland

Bibliografia

• [1] E. D. Gluskin, Diameter of the Minkowski compactum is approximately equal to n, Funct. Anal. Appl. 15 (1981), 57–58.
• [2] B. Grünbaum, Measures of symmetry for convex sets, 1963 Proc. Sympos. Pure Math., Vol. VII, 233–270, Amer. Math. Soc., Providence, R.I.
• [3] F. John, Extremum problems with inequalities as subsidiary conditions, Courant Anniversary Volume, 1948, 187–204.
• [4] M. Lassak, Approximation of convex bodies by triangles, Proc. Amer. Math. Soc. 115 (1992), 207–210.
• [5] M. Lassak, Banach–Mazur distance of planar convex bodies, Aequationes Math. 74 (2007), 282–286.
• [6] W. Stromquist, The maximum distance between two-dimensional Banach spaces, Math. Scand. 48 (1981), 205–225.
• [7] S. J. Szarek, Convexity, complexity and high dimensions, Proceedings of the International Congress of Mathematicians, Madrid, Spain, August 22–30, 2006, Volume II: Invited Lectures, Zürich: European Mathematical Society (EMS), 1599–1621.
• [8] N. Tomczak-Jaegermann, Banach–Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics 38, Longman Scientifical and Technical, New York, 1989.