A geometric characterization of inner product spaces

1980 ◽  
Vol 37 (1-2) ◽  
pp. 84-91
Author(s):  
Leonard E. Dor
Keyword(s):  
Geometric Characterization ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

A characterization of inner product spaces based on a property of height's transformation

1993 ◽  
Vol 61 (6) ◽  
pp. 560-566 ◽  
Author(s):  
C. Alsina ◽  
P. Guijarro ◽  
M. S. Tom�s
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

scholarly journals Hyperstability of the Fréchet Equation and a Characterization of Inner Product Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Anna Bahyrycz ◽  
Janusz Brzdęk ◽  
Magdalena Piszczek ◽  
Justyna Sikorska
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Fréchet Equation ◽  
New Inequalities

We prove some stability and hyperstability results for the well-known Fréchet equation stemming from one of the characterizations of the inner product spaces. As the main tool, we use a fixed point theorem for the function spaces. We finish the paper with some new inequalities characterizing the inner product spaces.

scholarly journals On Carlsson type orthogonality and characterization of inner product spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 859-870 ◽  
Author(s):  
Eder Kikianty ◽  
Sever Dragomir
Keyword(s):  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Isosceles Orthogonality ◽  
Inner Product Spaces ◽  
Pythagorean Orthogonality

In an inner product space, two vectors are orthogonal if their inner product is zero. In a normed space, numerous notions of orthogonality have been introduced via equivalent propositions to the usual orthogonality, e.g. orthogonal vectors satisfy the Pythagorean law. In 2010, Kikianty and Dragomir [9] introduced the p-HH-norms (1 ? p < ?) on the Cartesian square of a normed space. Some notions of orthogonality have been introduced by utilizing the 2-HH-norm [10]. These notions of orthogonality are closely related to the classical Pythagorean orthogonality and Isosceles orthogonality. In this paper, a Carlsson type orthogonality in terms of the 2-HH-norm is considered, which generalizes the previous definitions. The main properties of this orthogonality are studied and some useful consequences are obtained. These consequences include characterizations of inner product space.

Sign in / Sign up

Export Citation Format

Share Document