|
|||||
|
|
Another approach to characterizations of generalized triangle inequalities in normed spaces |
|
| Authors: | Tamotsu Izumida Ken-Ichi Mitani Kichi-Suke Saito |
| Institution: | 1. Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, Niigata, 950-2181, Japan 2. Department of Information and Communication Engineering, Faculty of Computer Science and System Engineering, Okayama Prefectural University, Okayama, 719-1197, Japan 3. Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan |
| Abstract: | 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, ..., µ n ) ∈ ? n 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]. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |