Open AccessAn extension of the schwarz inequality in inner product spaces
Author(s) -
Yun Ye
Publication year - 2018
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1815329y
Subject(s) - mathematics , extension (predicate logic) , inner product space , tuple , product (mathematics) , inequality , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , geometry , computer science , programming language
We extend the improved Schwarz inequality of Dragomir [1, Theorem 2] to any power p ? 2, ||x||p||y||p-|?x,y?|p ? |det [|?x,e?| |?y,e?|(||y||p - |?x,e?|p)1/p (||y||p- |?y,e?|p)1/p]|p for any vectors x, y, e ? Cn with ||e|| = 1. Applications to n-tuples of complex numbers are also included.