[PDF] Top 20 A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation

... 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 ... See full document

... The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy ...the ... See full document

... (2010) Stability of a Mixed Type Functional Equa- tion on Multi-Banach Spaces: A Fixed Point ...Approach. Fixed Point Theory and Applications , 2010, Article ID: ...The ... See full document

... the functional equation (12) is not stable for r = 1 in Corollaries ...a additive mapping A : C → C and a constant d > 0 such that |g(x) − A(x)| ≤ d|x| for all x ∈ C ... See full document

... Jun and Kim proved that a function f between real vector spaces X and Y is a solution of 1.5 if and only if there exists a unique function C : X × X × X → Y such that fx Cx, x, x for all x ∈ X, and C is symmetric for ... See full document

... a functional equation was first posed by Ulam [16] which was answered by Hyers [17] under the assumption that the groups are Banach ...the stability problem with unbounded Cauchy ... See full document

... the stability of group homomorphisms was proposed by Ulam 1: Under what conditions does there exist a group homomorphism near an approximately group homomorphism? In 1941, Hyers 2 considered the case of ... See full document

... A fixed-point approach to the stability of a functional equation on quadratic forms Jae-Hyeong Bae1 and Won-Gil Park2* * Correspondence: [email protected] 2 Department of Mathematics E[r] ... 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

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

... The stability problem of functional equations originated from a question of Ulam 13 concerning the stability of group ...for additive mappings and by ...Hyers-Ulam stability or as ... 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 ... See full document

... On quadratic set-valued ...s functional equation for set-valued ...of additive selection for ( α, β )-( β, α ) type subadditive set-valued ... 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

... 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

... first stability problem concerning group ...for additive mappings. For additive mapping involving dif- ferent powers of norms ...This stability is also investigates by Park ...a fuzzy ... See full document

... of stability problems for functional equations is linked to the renowned Ulam problem [34] (in 1940), concerning the stability of group homomorphisms, which was first elucidated by Hyers [10], in ... See full document

... Cauchy functional equation f(x + y) = f(x) + f(y), 〈 x, y 〉 = ...additivity equation everywhere. Thus, orthogonal Cauchy equation is not equivalent to the classic Cauchy equation on the ... 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 by S. ... See full document

... The stability problem of functional equations originated from a question of Ulam [1] concerning the stability of group ...for additive mappings and by Rassias [4] for linear mappings by ... See full document