Another approach to characterizations of generalized triangle inequalities in normed spaces

作者：Izumida Tamotsu^*; Mitani Ken Ichi; Saito Kichi Suke

来源：Central European Journal of Mathematics, 2014, 12(11): 1615-1623.

DOI：10.2478/s11533-014-0432-z

• Generalized triangle inequality
• Absolute norm
• psi-direct sum
• Generalized H lder inequality

In this paper, we consider a generalized triangle inequality of the following type: %26lt;br%26gt;vertical bar vertical bar x(1) +...+ x(0 vertical bar vertical bar)(p) %26lt;=vertical bar vertical bar x(1)vertical bar vertical bar(p)/mu 1 +...+ vertical bar vertical bar x(n)vertical bar vertical bar(p)/mu (for all x(1),...3x(n) is an element of X), %26lt;br%26gt;where (X, vertical bar vertical bar center dot vertical bar vertical bar) is a normed space, (mu(1),..., mu(n) ) a a%26quot;e (n) and p %26gt; 0. By using psi-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].

• 出版日期2014-11