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Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation
Arab Journal of Mathematical Sciences, 2015 We use the operatorial approach to obtain, in non-Archimedean spaces, the Hyers–Ulam stability of the Pexider K-quadratic functional equation∑k∈Kf(x+k·y)=κg(x)+κh(y),x,y∈E, where f,g,h:E→F are applications and K is a finite subgroup of the group of ...
A.B. Chahbi +3 more
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On the Stability of Quadratic Functional Equations [PDF]
Abstract and Applied Analysis, 2008 Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx-y) = 2k2f(x) + 2f(y) for all x, y ∈ X if and only if the mapping f : X → Y satisfies f(x + y) + f(x-y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, the Hyers‐Ulam‐Rassias stability of the above functional equation in Banach spaces is proven.
Jung Rye Lee, Jong Su An, Choonkil Park
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Quadratic functional equations of Pexider type [PDF]
International Journal of Mathematics and Mathematical Sciences, 2000 First, the quadratic functional equation of Pexider type will be solved. By applying this result, we will also solve some functional equations of Pexider type which are closely associated with the quadratic equation.
Soon-Mo Jung
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A variant of the quadratic functional equation on semigroups [PDF]
Proyecciones (Antofagasta), 2018 Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions f : S → H of the following variant of the quadratic functional equation f(xy) + f(σ(y)x) = 2f(x) + 2f(y)
B. Fadli, D. Zeglami, S. Kabbaj
semanticscholar +4 more sources
Approximate mixed type quadratic-cubic functional equation
AIMS Mathematics, 2021 In this paper, we investigate the generalized Hyers-Ulam stability of the following mixed type quadratic-cubic functional equation \begin{align*} 2f(2x+y)+2f(2x-y) = 4f(x+y)+4f(x-y)+4f(2x)+f(2y)-8f(x)-8f(y) \end{align*} in non-Archimedean $(n ...
Zhihua Wang
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Approximation on the Quadratic Reciprocal Functional Equation [PDF]
Journal of Function Spaces, 2014 The quadratic reciprocal functional equation is introduced. The Ulam stability problem for an ϵ-quadratic reciprocal mapping f:X→Y between nonzero real numbers is solved.
Abasalt Bodaghi, Sang Og Kim
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A Multidimensional Functional Equation Having Quadratic Forms as Solutions [PDF]
Journal of Inequalities and Applications, 2007 We obtain the general solution and the stability of the -variable quadratic functional equation The quadratic form is a solution of the given functional equation.
Bae Jae-Hyeong, Park Won-Gil
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Journal of Function Spaces, 2021 In this work, we have to introduce a generalized quadratic functional equation and derive its solution. The main objective of this work is to investigate the Hyers-Ulam stability of quadratic functional equation in non-Archimedean n,β-normed spaces.
Nazek Alessa +3 more
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Stability of an additive-quadratic-quartic functional equation
Demonstratio Mathematica, 2020 In this paper, we investigate the stability of an additive-quadratic-quartic functional ...
Kim Gwang Hui, Lee Yang-Hi
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On the stability of a quadratic Jensen type functional equation
Journal of Mathematical Analysis and Applications, 2002 For real linear spaces \(X\) and \(Y\), \(f: X\to Y\) satisfies the functional equation \[ 9f\Biggl({x+ y+ z\over 3}\Biggr)+ f(x)+ f(y)+ f(z)= 4\Biggl[f\Biggl({x+ y\over 2}\Biggr)+ f\Biggl({y+ z\over 2}\Biggr)+ f\Biggl({z+ x\over 2}\Biggr)\Biggr] \] if and only if \(f(x)= Q(x)+ A(x)+ B\) for an additive function \(A: X\to Y\), a quadratic function \(Q:
Young Whan Lee
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