TY - JOUR AU - Dragomir, S. S. PY - 2009/09/30 Y2 - 2024/03/29 TI - On some inequalities in normed linear spaces JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 40 IS - 3 SE - Papers DO - 10.5556/j.tkjm.40.2009.502 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/502 SP - 225-237 AB - Upper 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. ER -