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2014 | 12 | 11 | 1615-1623
Tytuł artykułu

Another approach to characterizations of generalized triangle inequalities in normed spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we consider a generalized triangle inequality of the following type: $$\left\| {x_1 + \cdots + x_n } \right\|^p \leqslant \frac{{\left\| {x_1 } \right\|^p }} {{\mu _1 }} + \cdots + \frac{{\left\| {x_2 } \right\|^p }} {{\mu _n }}\left( {for all x_1 , \ldots ,x_n \in X} \right),$$ where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
11
Strony
1615-1623
Opis fizyczny
Daty
wydano
2014-11-01
online
2014-06-29
Twórcy
Bibliografia
  • [1] Ansari A.H., Moslehian M.S., Refinements of reverse triangle inequalities in inner product spaces, J. Inequal. Pure Appl. Math., 2005, 6(3), article 64, 12pp.
  • [2] Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Characterizations 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
  • [3] Kato M., Saito K.-S., Tamura T., On ψ-direct sums of Banach spaces and convexity, J. Aust. Math. Soc., 2003, 75(3), 413–422 http://dx.doi.org/10.1017/S1446788700008193
  • [4] Kato M., Saito K.-S., Tamura T., Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl., 2007, 10(2), 451–460
  • [5] Maligranda L., Some remarks on the triangle inequality for norms, Banach J. Math. Anal., 2008, 2(2), 31–41
  • [6] Mitani K.-I., Oshiro S., Saito K.-S., Smoothness of ψ-direct sums of Banach spaces, Math. Ineq. Appl., 2005, 8(1), 147–157
  • [7] Mitani K.-I., Saito K.-S., On sharp triangle inequalities in Banach spaces II, J. Inequal. Appl., 2010, Art. ID 323609, 17pp.
  • [8] 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
  • [9] Nikolova L., Persson L.-E., Varošanec S., The Beckenbach-Dresher inequality in the -direct sums of spaces and related results, J. Inequal. Appl., 2012, 2012:7, 14pp. http://dx.doi.org/10.1186/1029-242X-2012-7
  • [10] Saito K.-S., Kato M., Takahashi Y., Von Neumann-Jordan constant of absolute normalized norms on ℂ2, J. Math. Anal. Appl., 2000, 244(2), 515–532 http://dx.doi.org/10.1006/jmaa.2000.6727
  • [11] Saito K.-S., Kato M., Takahashi Y., Absolute norms on ℂn, J. Math. Anal. Appl., 2000, 252(2), 879–905 http://dx.doi.org/10.1006/jmaa.2000.7139
  • [12] Takahasi S.-E., Rassias J.M., Saitoh S., Takahashi Y., Refined generalizations of the triangle inequality on Banach spaces, Math. Ineq. Appl., 2010, 13(4), 733–741
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0432-z
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