Baire category theorem and approximation of the Pexider quadratic functional equation on a set of Lebesgue measure zero

2018 ◽  
Vol 27 (3) ◽  
pp. 697-707
Author(s):  
Iz-iddine EL-Fassi ◽  
Abdellatif Chahbi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Lebesgue Measure ◽  
Measure Zero ◽  
Baire Category ◽  
Quadratic Functional Equation ◽  
Lebesgue Measure Zero ◽  
Quadratic Functional ◽  
Baire Category Theorem ◽  
Category Theorem

scholarly journals Stability of generalized quadratic functional equation on a set of measure zero

2015 ◽  
Vol 14 (1) ◽  
pp. 149-162
Author(s):  
Youssef Aribou ◽  
Hajira Dimou ◽  
Abdellatif Chahbi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Vector Space ◽  
Lebesgue Measure ◽  
Measure Zero ◽  
Quadratic Functional Equation ◽  
Lebesgue Measure Zero ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Complex Vector Space ◽  
Complex Vector

Abstract In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equationwhere E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation.

On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector

2016 ◽  
Vol 23 (3) ◽  
pp. 387-391
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Lebesgue Measure ◽  
Measure Zero ◽  
Baire Category ◽  
Lebesgue Measure Zero ◽  
The Difference

AbstractIt is shown that the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector can be of Lebesgue measure zero and of first Baire category. This result gives an answer to a question posed by G. Lazou.

The Baire category theorem and cardinals of countable cofinality

1982 ◽  
Vol 47 (2) ◽  
pp. 275-288 ◽  
Author(s):  
Arnold W. Miller
Keyword(s):  
Real Line ◽  
Measure Zero ◽  
Baire Category ◽  
The Other ◽  
Baire Category Theorem ◽  
The Real ◽  
Zero Sets ◽  
Category Theorem ◽  
Dense Sets ◽  
The Ideal

AbstractLet κB be the least cardinal for which the Baire category theorem fails for the real line R. Thus κB is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κB cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2ω1 be ℵω. Similar questions are considered for the ideal of measure zero sets, other ω1, saturated ideals, and the ideal of zero-dimensional subsets of Rω1.

scholarly journals Stability of Pexiderized quadratic functional equation on a set of measure zero

2016 ◽  
Vol 09 (06) ◽  
pp. 4554-4562 ◽  
Author(s):  
Iz-iddine EL-Fassi ◽  
Abdellatif Chahbi ◽  
Samir Kabbaj ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Measure Zero ◽  
Quadratic Functional Equation ◽  
Quadratic Functional
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