Fixed point theorems in probabilistic inner product spaces

1985 ◽  
Vol 6 (1) ◽  
pp. 67-74
Author(s):  
Zhang Shi-sheng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

scholarly journals The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Vector Space ◽  
Fixed Point Method ◽  
Inner Product ◽  
Product Spaces ◽  
Real Vector ◽  
Fixed Integer ◽  
Inner Product Spaces ◽  
Fuzzy Approximation

Th. M. Rassias (1984) proved that the norm defined over a real vector space is induced by an inner product if and only if for a fixed integer holds for all The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation which is said to be a functional equation associated with 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 Nonlinear fuzzy stability of a functional equation related to a characterization of inner product spaces via fixed point technique

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1067-1080
Author(s):  
Zhihua Wang ◽  
Prasanna Sahoo
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Fixed Point Technique ◽  
The Stability ◽  
Fuzzy Banach Space

Using the fixed point method, we prove some results concerning the stability of the functional equation 2n?i=1 f(xi-1/2n 2n?j=1 xj)=2n?i=1 f (xi)-2nf(1/2n 2n?i=1 xi) where f is defined on a vector space and taking values in a fuzzy Banach space, which is said to be a functional equation related to a characterization of inner product spaces.

scholarly journals Stability of a generalization of the Fréchet functional equation

2015 ◽  
Vol 14 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Renata Malejki
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Function Spaces ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
New Inequalities

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

scholarly journals Stability of the Fréchet Equation in Quasi-Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 490
Author(s):  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Inner Product ◽  
Main Role ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Fréchet Equation

We investigate the Hyers–Ulam stability of the well-known Fréchet functional equation that comes from a characterization of inner product spaces. We also show its hyperstability on a restricted domain. We work in the framework of quasi-Banach spaces. In the proof, a fixed point theorem due to Dung and Hang, which is an extension of a fixed point theorem in Banach spaces, plays a main role.

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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