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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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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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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 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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Quadratic--quartic functional equations in RN--spaces [PDF]
Journal of Inequalities and Applications, 2009 11 ...
M. Eshaghi Gordji +2 more
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Intuitionistic Fuzzy Stability of a Quadratic Functional Equation [PDF]
Fixed Point Theory and Applications, 2010 We consider the intuitionistic fuzzy stability of the quadratic functional equation by using the fixed point alternative, where is a positive integer.
Wang Liguang
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Fuzzy Stability of a Quadratic-Additive Functional Equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We investigate a fuzzy version of stability for the functional equation 𝑓(𝑥+𝑦+𝑧+𝑤)+2𝑓(𝑥)+2𝑓(𝑦)+2𝑓(𝑧)+2𝑓(𝑤)−𝑓(𝑥+𝑦)−𝑓(𝑥+𝑧)−𝑓(𝑥+𝑤)−𝑓(𝑦+𝑧)−𝑓(𝑦+𝑤)−𝑓(𝑧+𝑤)=0.
Sun Sook Jin, Yang Hi Lee
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On the stability of a quadratic Jensen type functional equation
Journal of Mathematical Analysis and Applications, 2002 AbstractIn this paper we obtain the general solution of the quadratic Jensen type functional equation 9fx+y+z3+f(x)+f(y)+f(z)=4fx+y2+fy+z2+fz+x2 and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Găvruta.
Young Whan Lee
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Jensen’s and the quadratic functional equations with an endomorphism [PDF]
Proyecciones (Antofagasta), 2017 We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Khalid Sabour, Samir Kabbaj
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