Author:
Izumida Tamotsu,Mitani Ken-Ichi,Saito Kichi-Suke
Abstract
AbstractIn 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].
Reference12 articles.
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
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
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
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