scholarly journals On the Boas-Bellman inequality in inner product spaces

2004 ◽  
Vol 69 (2) ◽  
pp. 217-225 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Bessel Inequality

New results related to the Boas–Bellman generalisation of Bessel' inequality in inner product spaces are given.

A Type of Orthonormal Bases on 2-*-Inner Product Spaces

2020 ◽  
Vol 57 (4) ◽  
pp. 541-551
Author(s):  
Behrooz Mohebbi Najmabadi ◽  
Tayebe Lal Shateri ◽  
Ghadir Sadeghi
Keyword(s):  
Product Space ◽  
Orthonormal Basis ◽  
Dense Subset ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Orthonormal Bases ◽  
Inner Product Spaces ◽  
Bessel Inequality

In this paper, we define an orthonormal basis for 2-*-inner product space and obtain some useful results. Moreover, we introduce a 2-norm on a dense subset of a 2-*-inner product space. Finally, we obtain a version of the Selberg, Buzano’s and Bessel inequality and its results in an A-2-inner product space.

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
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