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 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 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 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.

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
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