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2013 | 11 | 7 | 1212-1227
Tytuł artykułu

On the calculation of the Dunkl-Williams constant of normed linear spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the Dunkl-Williams constant DW(X) of a normed linear space X. In this paper we present some characterizations of this constant. As an application, we calculate DW(ℓ2-ℓ∞) in the Day-James space ℓ2-ℓ∞.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
7
Strony
1212-1227
Opis fizyczny
Daty
wydano
2013-07-01
online
2013-04-26
Twórcy
  • Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, Niigata, 950-2181, Japan, mizuguchi@m.sc.niigata-u.ac.jp
Bibliografia
  • [1] Alonso J., Some properties of Birkhoff and isosceles orthogonality in normed linear spaces, In: Inner Product Spaces and Applications, Pitman Res. Notes Math. Ser., 376, Longman, Harlow, 1997, 1–11
  • [2] Alonso J., Martini H., Mustafaev Z., On orthogonal chords in normed planes, Rocky Mountain J. Math., 2011, 41(1), 23–35 http://dx.doi.org/10.1216/RMJ-2011-41-1-23[Crossref]
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  • [5] Dadipour F., Fujii M., Moslehian M.S., Dunkl-Williams inequality for operators associated with p-angular distance, Nihonkai Math. J., 2010, 21(1), 11–20
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  • [7] Day M.M., Some characterizations of inner-product spaces, Trans. Amer. Math. Soc., 1947, 62, 320–337 http://dx.doi.org/10.1090/S0002-9947-1947-0022312-9[Crossref]
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  • [10] James R.C., Inner product in normed linear spaces, Bull. Amer. Math. Soc., 1947, 53(6), 559–566 http://dx.doi.org/10.1090/S0002-9904-1947-08831-5[Crossref]
  • [11] James R.C., Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 1947, 61(2), 265–292 http://dx.doi.org/10.1090/S0002-9947-1947-0021241-4[Crossref]
  • [12] Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310 http://dx.doi.org/10.1016/j.jmaa.2007.11.045[Crossref][WoS]
  • [13] Kato M., Saito K.-S., Tamura T., Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl., 2007, 10(2), 451–460
  • [14] Kirk W.A., Smiley M.F., Another characterization of inner product spaces, Amer. Math. Monthly, 1964, 71(8), 890–891 http://dx.doi.org/10.2307/2312400[Crossref]
  • [15] Megginson R.E., An Introduction to Banach Space Theory, Grad. Texts in Math., 183, Springer, New York, 1998 http://dx.doi.org/10.1007/978-1-4612-0603-3[Crossref]
  • [16] Moslehian M.S., Dadipour F., Rajic R., Maric A., A glimpse at the Dunkl-Williams inequality, Banach J. Math. Anal., 2011, 5(2), 138–151
  • [17] Nilsrakoo W., Saejung S., The James constant of normalized norms on R2, J. Inequal. Appl., 2006, #26265
  • [18] Pečaric J., Rajic R., Inequalities of the Dunkl-Williams type for absolute value operators, J. Math. Inequal., 2010, 4(1), 1–10 http://dx.doi.org/10.7153/jmi-04-01[Crossref]
  • [19] Saito K.-S., Tominaga M., A Dunkl-Williams type inequality for absolute value operators, Linear Algebra Appl., 2010, 432(12), 3258–3264 http://dx.doi.org/10.1016/j.laa.2010.01.016[WoS][Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0238-4
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