[PDF] Top 20 Stability of Quadratic Functional Equations via the Fixed Point and Direct Method

... of functional equations which generalize the Hyers’ ...similar stability theorem for the unbounded Cauchy difference controlled by a product of unbounded function εx p ... See full document

... Rassias stability of quartic functional equation f (3 x  y )  f x (  3 ) y  64 ( ) f x  64 ( ) f y  24 ( f x  y ) 6 (  f x  y ) in the setting of random normed space and intuitionistic random ... See full document

... a fixed constant. The solution of 3.1 and a generalized stability result in Ulam-Hyers sense for the above equation are given in 35, by the direct ... See full document

... to functional equations 14, 20. A comparison between the direct method and fixed alternative method for functional equations is given in ...The fixed ... See full document

... a quadratic functional ...tic functional equation is said to be a quadratic ...Hyers-Ulam stability of the quadratic functional equation was proved by Skof [24] for ... See full document

... new method, successively developed in [8-10], to obtaining the existence of the exact solutions and the error estimations, based on the fixed point ...The stability of several ... See full document

... of functional equations is as ...a functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by Ulam 1 in ... See full document

... for all x ∈ X. It follows from (.) that d(f , Jf ) ≤ . So, we obtain inequality (.). The rest of the proof is similar to the proofs of Theorems . and .. Corollary . Let θ be a positive real number and p be a ... See full document

... of stability problems for functional equations is related to a question of Ulams[24] concerning the stability of group homomorphism’s was affirmatively answered for Banach spaces by ... See full document

... The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group ...Hyers-Ulam stability or as Hyers-Ulam-Rassias stability ... See full document

... Under what condition is there a homomorphism near an approximately homomorphism between a group and a metric group? This is called the stability problem of functional equations which was first raised ... See full document

... the fixed point method to prove the Hyers-Ulam-Rassias stability of the functional equation ...Hyers-Ulam-Rassias stability approach for the proof of new fixed ... See full document

... Hyers’ theorem was generalized by Aoki 15 for additive mappings and by Th. M. Rassias 16 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. M. Rassias 16 has provided a lot of influence in ... See full document

... The stability problem of functional equations originated from the following question of Ulam [18]: Under what condition does there exist an additive mapping near an approximately additive mapping? In ... See full document

... Hyers-Ulam stability to a number of functional equations and mappings see ...A quadratic functional equation is a functional equation of the following ... See full document

... of stability problem for functional equations goes back to a question raised by Ulam [44] concerning the stability of group homomorphisms that affirmatively answered for Banach spaces by Hyers ... See full document

... E is replaced by an Abelian group it was delt by P.W.Choelewa [10].S.Czerwik [11,12] proved the Hyer-Ulam-Rassias stability of the quadratic functional equation.This result further generalized by ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with applica- ...using fixed point methods, the stability problems of several ... See full document

... a functional equation (ζ ) is stable if any function g satisfying the equation (ζ ) approximately is near to the true solution of (ζ ...a functional equation is su- perstable if every approximate solution ... See full document

... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group ...Hyers-Ulam stability of functional ...The stability ... See full document