scholarly journals Measure zero stability problem of a new quadratic functional equation

2016 ◽  
Vol 433 (2) ◽  
pp. 948-956
Author(s):  
Jaeyoung Chung ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Stability Problem ◽  
Measure Zero ◽  
Quadratic Functional Equation ◽  
Quadratic Functional

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

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.

scholarly journals On alienation of two functional equations of quadratic type

2021 ◽  
Author(s):  
Roman Ger
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Real Numbers ◽  
Alpha Beta ◽  
Beta 2 ◽  
Special Case

Abstract  We deal with an alienation problem for an Euler–Lagrange type functional equation $$\begin{aligned} f(\alpha x + \beta y) + f(\alpha x - \beta y) = 2\alpha ^2f(x) + 2\beta ^2f(y) \end{aligned}$$ f ( α x + β y ) + f ( α x - β y ) = 2 α 2 f ( x ) + 2 β 2 f ( y ) assumed for fixed nonzero real numbers $$\alpha ,\beta ,\, 1 \ne \alpha ^2 \ne \beta ^2$$ α , β , 1 ≠ α 2 ≠ β 2 , and the classic quadratic functional equation $$\begin{aligned} g(x+y) + g(x-y) = 2g(x) + 2g(y). \end{aligned}$$ g ( x + y ) + g ( x - y ) = 2 g ( x ) + 2 g ( y ) . We were inspired by papers of Kim et al. (Abstract and applied analysis, vol. 2013, Hindawi Publishing Corporation, 2013) and Gordji and Khodaei (Abstract and applied analysis, vol. 2009, Hindawi Publishing Corporation, 2009), where the special case $$g = \gamma f$$ g = γ f was examined.

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