A note on “Some inequalities in inner product spaces related to the generalized triangle inequality” by S.S. Dragomir et al.

2011 ◽  
Vol 217 (22) ◽  
pp. 9497-9498
Author(s):  
Ángel Plaza ◽  
Kishin Sadarangani
Keyword(s):  
Triangle Inequality ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Generalized Triangle Inequality

scholarly journals More on reverse triangle inequality in inner product spaces

2005 ◽  
Vol 2005 (18) ◽  
pp. 2883-2893 ◽  
Author(s):  
A. H. Ansari ◽  
M. S. Moslehian
Keyword(s):  
Product Space ◽  
Triangle Inequality ◽  
Schwarz Inequality ◽  
Unit Vector ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Generalized Triangle Inequality

Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that ifais a unit vector in a real or complex inner product space(H;〈.,.〉),r,s>0,p∈(0,s],D={x∈H,‖rx−sa‖≤p},x1,x2∈D−{0}, andαr,s=min{(r2‖xk‖2−p2+s2)/2rs‖xk‖:1≤k≤2}, then(‖x1‖‖x2‖−Re〈x1,x2〉)/(‖x1‖+‖x2‖)2≤αr,s.

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

Triangle Congruence Characterizations of Inner Product Spaces

1989 ◽  
Vol 144 (1) ◽  
pp. 81-86
Author(s):  
Charles R. Diminnie ◽  
Edward Z. Andalafte ◽  
Raymond W. Freese
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces
Sign in / Sign up

Export Citation Format

Share Document