Abstract:In this paper, we consider a generalized triangle inequality of the following type:where (X · ) is a normed space, (µ 1 µ ) ∈ R and > 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]. MSC:46B20, 46B25

, 1 ∈ X . Here we study when this norm inequality attains equality in strictly convex Banach spaces. MSC:46B20, 46B99, 26D20