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Another approach to characterizations of generalized triangle inequalities in normed spaces

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Izumida T., Mitani K.-I., Saito K.-S.

Open Mathematics

2014

tom 12

nr 11

1615-1623

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].

Ograniczanie wyników

1 Open Mathematics

1 Izumida T.

1 Mitani K.-I.

1 Saito K.-S.

1 2014

Wyniki wyszukiwania

Another approach to characterizations of generalized triangle inequalities in normed spaces