scholarly journals Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory

10.37236/330 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Chunrong Feng ◽  
Liangpan Li ◽  
Jian Shen
Keyword(s):  
Probability Theory ◽  
Functional Analysis ◽  
Finite Field ◽  
Best Approximation ◽  
Approximation Theorem ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
The Best Approximation

The main purpose of this paper is to show that many inequalities in functional analysis, probability theory and combinatorics are immediate corollaries of the best approximation theorem in inner product spaces. Besides, as applications of the de Caen-Selberg inequality, the finite field Kakeya and Nikodym problems are also studied.

scholarly journals Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hacer Bozkurt ◽  
Sümeyye Çakan ◽  
Yılmaz Yılmaz
Keyword(s):  
Functional Analysis ◽  
Nonlinear Analysis ◽  
Linear Functional ◽  
Fréchet Derivative ◽  
Inner Product ◽  
Product Spaces ◽  
Frechet Derivative ◽  
Inner Product Spaces

Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986)). Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005), Talo and Başar (2010), and Nikol'skiĭ (1993)). His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.

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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