On the stability of the quadratic mapping in normed spaces.

By Gwang Hui Kim. 2001

340 citations recorded by the source corpus.

The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and alsothe sta- bility in the spirit of Gavruta for each of the following quadratic functional equations f( x+ y)+ f( x− y) = 2 f( x)+ 2 f( y), f( x+ y + z) + f( x− y)+ f( y− z) + f( z− x) = 3 f( x)+3 f( y)+3 f( z), f (x+y +z)+ f( x)+ f( y)+ f( z)= f( x+y)+ f( y+z)+ f( z+x) are investigated.

Subfields: Applied Mathematics

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In Applied Mathematics

Citations in the corpus

The Generalized Hyers--Ulam--Rassias Stability of a Cubic Functional Equation (2007, background): “Under the assumption that f(tx) is continuous in t ∈ R for each fixed x ∈ X, by the same reasoning as the proof of [4], the cubic function T : X → Y satisfies T (tx) = t(3)T (x) for all t ∈ R, x ∈ X.”
Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces (2008, background): “In [4], Czerwik proved the generalized Hyers-Ulam stability of the quadratic functional equation.”
The stability of a cubic type functional equation with the fixed point alternative (2005, background): “The quadratic functionf (x) = cx2 is a solution of this functional equation, and so o usually is said the above functional equation to be quadratic [1,5,11,13].”
Solution and stability of generalized mixed type cubic , quadratic and additive functional equation in quasi-Banach spaces (2008, background): “In the paper [5] , Czerwik proved the Hyers-Ulam-Rassias stability of the equation (1.”
On the orthogonal stability of the pexiderized quadratic equation (2004, positive): “Czerwik [4] in the spirit of Hyers–Ulam–Rassias.”
Elementary remarks on Ulam–Hyers stability of linear functional equations (2007, background): “Many of them treat functional equations in several variables and what is given is an inequality in several variables and the first step in order to prove stability consists in certain manipulations transforming that inequality in several variables in an inequality in one variable (see, for instance,”
Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras (2008, background): “Găvruta [10], Czerwik [7], who among others studied the Hyers–Ulam stability of functional equations.”
Quadratic-Quartic Functional Equations in RN-Spaces (2009, background): “In [7], Czerwik proved the Hyers-Ulam-Rassias stability of the functional equation (1.”
STABILITY OF FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN SPACES (2007, background): “In [6], Czerwik proved the generalized Hyers–Ulam stability of the quadratic functional equation.”
On the Ulam stability of Jensen and Jensen type mappings on restricted domains (2003, background): “Other inter stability results have been achieved also by the following authors: Aczél [1], Borell Forti [2,9], Cholewa [4], Czerwik [5], Drljevic [6], and Kannappan [15].”
A fixed point approach to stability of a quadratic equation (2005, positive): “Czerwik [5] in the spirit of Hyers–Ulam–Rassias.”
Asymptotic behavior of alternative Jensen and Jensen type functional equations (2005, result): “Other interesting stability results have been achieved also by the following authors J. Aczél [1], C. Borelli and G.L. Forti [2] [9], P.W. Cholewa [4], St. Czerwik [5], and H. Drljevic [6].”
The generalized Hyers–Ulam–Rassias stability of a cubic functional equation☆ (2002, background): “The proof of the last assertion in the above corollary goes through in the same way as that of [4].”