@article{3064869, title = "Refined generalizations of the triangle inequality on banach spaces", author = "Takahasi, S.-E. and Rassias, J.M. and Saitoh, S. and Takahashi, Y.", journal = "Mathematical Inequalities and Applications", year = "2010", volume = "13", number = "4", pages = "733-741", publisher = "Element D.O.O.", issn = "1331-4343, 1848-9966", doi = "10.7153/mia-13-52", abstract = "Let X be a complex Banach space and p a real number with p ≥ 1. We give a necessary and sufficient condition for complex numbers a, b and real numbers λ, μ and μ in order that the inequality [Equation presented] holds for every x, y ∈ X." }