Displaying similar documents to “Solution of nonlinear functional equations in linear normed spaces”

Another approach to characterizations of generalized triangle inequalities in normed spaces

Tamotsu Izumida, Ken-Ichi Mitani, Kichi-Suke Saito (2014)

Open Mathematics

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In this paper, we consider a generalized triangle inequality of the following type: x 1 + ⋯ + x n p ⩽ x 1 p μ 1 + ⋯ + x 2 p μ n f o r a l l x 1 , ... , x n ∈ X , 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].