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2014 | 12 | 5 | 778-786
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Characterization of intermediate values of the triangle inequality II

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EN
Abstrakty
EN
In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C n that satisfy 0 ≤ C n ≤ Σj=1n ‖x j‖ − ‖Σj=1n x j‖, x 1,...,x n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
5
Strony
778-786
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-02-15
Twórcy
autor
Bibliografia
  • [1] Abramovich Y.A., Aliprantis C.D., Problems in Operator Theory, Grad. Stud. in Math., 51, American Mathematical Society, Providence, 2002
  • [2] Ansari A.H., Moslehian M.S., More on reverse triangle inequality in inner product spaces, Int. J. Math. Math. Sci., 2005, 18, 2883–2893 http://dx.doi.org/10.1155/IJMMS.2005.2883
  • [3] Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Characterization of a generalized triangle inequality in normed spaces, Nonlinear Anal., 2012, 75(2), 735–741 http://dx.doi.org/10.1016/j.na.2011.09.004
  • [4] Dragomir S.S., Reverses of the triangle inequality in Banach spaces, JIPAM. J. Inequal. Pure Appl. Math., 2005, 6(5), #129
  • [5] Dragomir S.S., Generalizations of the Pečarić-Rajić inequality in normed linear spaces, Math. Inequal. Appl., 2009, 12(1), 53–65
  • [6] Fujii M., Kato M., Saito K.-S., Tamura T., Sharp mean triangle inequality, Math. Inequal. Appl., 2010, 13(4), 743–752
  • [7] Hsu C.-Y., Shaw S.-Y., Wong H.-J., Refinements of generalized triangle inequalities, J. Math. Anal. Appl., 2008, 344(1), 17–31 http://dx.doi.org/10.1016/j.jmaa.2008.01.088
  • [8] Kato M., Saito K.-S., Tamura T., Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl., 2007, 10(2), 451–460
  • [9] Maligranda L., Some remarks on the triangle inequality for norms, Banach J. Math. Anal., 2008, 2(2), 31–41
  • [10] Martirosyan M.S., Samarchyan S.V., Inversion of the triangle inequality in ℝn, J. Contemp. Math. Anal., 2003, 38(4), 56–61
  • [11] Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035
  • [12] Mitani K.-I., Saito K.-S., On sharp triangle inequalities in Banach spaces II, J. Inequal. Appl., 2010, #323609
  • [13] Mitani K.-I., Saito K.-S., Kato M., Tamura T., On sharp triangle inequalities in Banach spaces, J. Math. Anal. Appl., 2007, 336(2), 1178–1186 http://dx.doi.org/10.1016/j.jmaa.2007.03.036
  • [14] Mizuguchi H., Saito K.-S., Tanaka R., On the calculation of the Dunkl-Williams constant of normed linear spaces, Cent. Eur. J. Math., 2013, 11(7), 1212–1227 http://dx.doi.org/10.2478/s11533-013-0238-4
  • [15] 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
  • [16] Ohwada T., On a continuous mapping and sharp triangle inequalities, In: Inequalities and Applications 2010, International Series of Numerical Mathematics, 161, Springer, Basel, 2011, 125–136
  • [17] Saito K.-S., Mitani K.-I., On sharp triangle inequalities in Banach spaces and their applications, In: Banach and Function Spaces III, Yokohama Publications, Yokohama, 2011, 295–304
  • [18] Saitoh S., Generalizations of the triangle inequality, JIPAM. J. Inequal. Pure Appl. Math., 2003, 43), #62
  • [19] Zhang L., Ohwada T., Chō M., Reverses of the triangle inequality in inner product spaces, Math. Inequal. Appl. (in press)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0369-7
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