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.

Projective actions, invariant sigma-curves and quadratic functional equations

1985 ◽  
Vol 98 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Patrick J. McCarthy
Keyword(s):  
Functional Equation ◽  
Periodic Function ◽  
Functional Equations ◽  
Continuous Solution ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Continuous Solutions ◽  
Linear Map

AbstractThe quadratic functional equation f(f(x)) *–Tf(x) + Dx = 0 is equivalent to the requirement that the graph be invariant under a certain linear map The induced projective map is used to show that the equation admits a rich supply of continuous solutions only when L is hyperbolic (T2 > 4D), and then only when T and D satisfy certain further conditions. The general continuous solution of the equation is given explicitly in terms of either (a) an expression involving an arbitrary periodic function, function additions, inverses and composites, or(b) suitable limits of such solutions.

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