On some inequalities in normed linear spaces
AbstractUpper and lower bounds for the norm of a linear combination of vectors are given. Applications in obtaining various inequalities for the quantities $ \Vert x / \Vert x \Vert -y / \Vert y \Vert \Vert $ and $ \Vert x/ \Vert y \Vert -y/ \Vert x \Vert \Vert $, where $ x $ and $ y $ are nonzero vectors, that are related to the Massera-Schaffer and the Dunkl-Williams inequalities are also provided. Some bounds for the unweighted Cebysev functional are given as well.
How to Cite
Dragomir, S. S. (2009). On some inequalities in normed linear spaces. Tamkang Journal of Mathematics, 40(3), 225-237. https://doi.org/10.5556/j.tkjm.40.2009.502