We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-1,
author = {C.-S. Lin},
title = {On (a,b,c,d)-orthogonality in normed linear spaces},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {1-10},
zbl = {1085.46019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-1}
}
C.-S. Lin. On (a,b,c,d)-orthogonality in normed linear spaces. Colloquium Mathematicae, Tome 103 (2005) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-1/