[PDF] Top 20 Refined stability of additive and quadratic functional equations in modular spaces

... linear spaces and the related theory of modular linear spaces have been established by Nakano in  ...and modular spaces is widely applied in the study of interpolation theory [, ... See full document

... normed spaces, and let f : X → Y be an arbitrarily given ...an additive, a quadratic, a cubic, a quadratic-additive, a cubic-additive, a cubic-quadratic, or a ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with ...the stability problems of several functional equations have been extensively ... See full document

... The stability problem concerning the stability of group homomorphisms of functional equations was originally introduced by Ulam [] in ...Ulam stability prob- lem was partially solved ... See full document

... The stability problem of functional equations originated from a question of Ulam [1] concerning the stability of group ...Banach spaces. Hyers ’ theorem was generalized by Aoki [3] for ... See full document

... Hyers-Ulam stability of the functional Equation ...normed spaces. The stability problems of several functional equations have been extensively investigated by a number of ... See full document

... Banach spaces. Hyers’s Theorem was generalized by Aoki [3] for additive map- pings and by Rassias [4] for linear mappings by considering an unbounded Cauchy ...Hyers-Ulam-Rassias stability of ... 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

... of quadratic, cubic and quartic functional equations and its Hyers-Ulam-Rassias stability were discussed by various authors ([3], [7], [12], [21], [24], [27], [29], [32], [34], ...of ... See full document

... The stability problem for functional equations started with the famous question of Ulam [15]: Under what conditions does there exist an additive function near an approximately additive ... See full document

... Hyers-Ulam stability problem for the quadratic functional equa- tion was proved by Skof [] for mappings f : X → Y , where X is a normed space and Y is a Banach ...Hyers-Ulam stability of the ... See full document

... The stability problem of functional equations is originated from a question of Ulam 11 concerning the stability of group ...Banach spaces. Hyers’ theorem was generalized by Aoki 13 for ... See full document

... The stability problem of functional equations originated from the following question of Ulam [13]: Under what condition does there exist an additive mapping near an approxi- mately ... See full document

... since n−1 j0 1/22 p /4 j 2 p /2 j ≤ 24 − 2 p 2 − 2 p /4 − 2 p 2 − 2 p . Because 0 < ε < 1 is arbitrary, we get inequality 2.3 in this case. Finally, to prove the uniqueness of F, let F : X → Y be another ... See full document

... a quadratic functional ...a quadratic mapping. A Hyers-Ulam stability pro- blem for the quadratic functional equation was proved by Skof [5] for mappings f : X → Y , where X is a ... See full document

... In recent years, the fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering. This new theory was introduced by Zadeh [1], in 1965 and since then a large number of ... See full document

... Therefore, f satisfies (.). Now, we claim that the functional equation (.) is not stable for p =  in Corollary .. Suppose, on the contrary, that there exist an additive mapping A : C → C and a ... See full document

... of functional equations is the following: ”when is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the ...for additive mapping ... See full document

... Hyers 2 proved the stability problem of additive mappings in Banach spaces. Rassias 3 provided a generalization of Hyers theorem which allows the Cauchy difference to be unbounded: let f : E → E be a ... See full document

... Ulam stability problem: When is it true that by slightly changing the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true? In [19], Hyers gave the first ... See full document