[PDF] Top 20 16. A quadratic type functional equation

... The Hyers–Ulam stability of the quadratic equation (1.1) was proved by Skof [22]. Cholewa [6] noticed that the theorem of Skof is still true if the relevant domain 𝒳 is replaced by an abelian group. ... See full document

... of functional equations for the proof of new fixed-point theorems with ...several functional equations have been extensively investigated by a number of authors see ... See full document

... and after taking the limit in the resulting inequality, we see that Q satisfies (.). Using a similar method to the proof of Theorem . we see that Q is the unique quadratic mapping satisfying (.). Now letting ... See full document

... other words, under what condition does there exist a homomorphism near an approximate homomorphism? The concept of stability for functional equation arises when we replace the functional ... See full document

... The stability problem of functional equations originated from a question of Ulam [1] concerning the stability of group homomorphisms. Hyers [2] gave a first affirmative answer to the question of Ulam for Banach ... See full document

... Cauchy functional equation f(x + y) = f(x) + f(y), namely, they showed that if f is a mapping from an orthogonality space X into a real Banach space Y and ||f(x + y) - f(x) - f(y)|| ≤ ε for all x, y Î X ... See full document

... for Equation 1.5 in non-Archimedean normed spaces. Euler-Lagrange type func- tional equations in various spaces have been constantly studied by many ... See full document

... Using the idea of intuitionistic fuzzy metric spaces introduced by Park 14 and Saadati and Park 15, 16, a new notion of intuitionistic fuzzy metric spaces with the help of the notion of continuous t-representable ... See full document

... Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4. In ... See full document

... a quadratic functional equation because the quadratic function f (x) = ax 2 is a solu- tion of the functional equation ...A quadratic functional equation was ... See full document

... f ( x + ay ) + a f ( x − y ) = f ( x − ay ) + a f ( x + y ) (1.2) for any positive integer a with a 6= − 1, 0, 1 was discussed by K.W. Jun and H.M. Kim [20]. Also, A. Najati and M.B. Moghimi [33] investigated the ... See full document

... of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, ... See full document

... called quadratic functional equation, and each of its solutions is said to be a quadratic ...the quadratic functional equation ... See full document

... Banach space. He proved that if f is a mapping between Banach spaces satisfying f (x + y) – f (x) – f (y) ≤ for some fixed ≥ , then there exists a unique additive mapping A such that f (x) – A(x) ≤ . In , Rassias [] ... See full document

... the quadratic functional ...the quadratic functional equation is said to be quadratic ...of functional equations for the proof of new fixed point theorems with ...several ... See full document

... In [16], Kenary and Cho proved the Hyers-Ulam-Rassias stability of mixed additive-quadratic Jensen type functional equation in non-Archimedean normed spaces and random normed spaces.. in[r] ... See full document

... Cauchy functional equation f(x + y) = f(x) + f(y), namely, they showed that if f is a mapping from an orthogonality space X into a real Banach space Y and ||f(x + y) - f(x) - f(y) || ≤ ε for all x, y Î X ... See full document

... 13. Nikodem, K: On quadratic set-valued functions. Publ Math Debrecen. 30, 297 – 301 (1984) 14. Nikodem, K: On Jensen ’ s functional equation for set-valued functions. Radovi Mat. 3, 23 – 33 (1987) ... See full document

... of functional equations ...Cauchy equation was proved by Brzdek [4]. The functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y) is called the quadratic functional ...the ... See full document

... the functional equation 1.7. In the sequel, we investigate the general solution of functional equation 1.7 when f is a function between vector spaces, and then we prove the generalized ... See full document