[PDF] Top 20 Orthogonal stability of an additive quartic functional equation with the fixed point alternative

... in which ⊥ is an abstract orthogonality relation, was first investigated by Gudder and Strawther [3]. They defined ⊥ by a system consisting of five axioms and described the general semi-continuous real-valued solution of ... See full document

... the stability of the linear functional ...the stability of the linear mapping in Banach ...S: Functional Equations and Inequalities in Several ...S: Stability of Functional ... See full document

... the orthogonal stability of the 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 ... See full document

... fixed point alternative and the stability of functional ...equations. Fixed Point Theory 4(1), 91-96 (2003) ...the stability of the linear mapping in Banach ...the ... See full document

... the stability of the additive mapping as a special ...Hyers-Ulam stability for the linear mapping between Banach spaces was ...Hyers-Ulam stability of the additive mapping was proved by ... 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) 15. ... See full document

... the functional equation ...Hyers stability of the additive functional equation ...and fixed point methods are respectively ...the additive functional ... See full document

... non-linear functional analysis involved is the stability problem of functional equations as follows: “When is it true that a mathematical object satisfying a certain property approximately must be ... See full document

... Hyers-Ulam stability of the additive-quadratic-cubic functional ...Hyers-Ulam stability of the additive-quadratic- cubic functional ... See full document

... the stability of functional equation was first suggested by Hyers 17 while he was trying to answer the question originated from the problem of Ulam 18, and it is called a direct method because it ... See full document

... Let (X, D) be a generalized metric space. An operator T : X → X satisfies a Lipschitz condition with Lipschitz constant L if there exists a constant L ≥  such that d(Tx, Ty) ≤ Ld(x, y) for all x, y ∈ X. If the Lipschitz ... 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 equation?” If 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

... Hyers-Ulam stability of the Cauchy additive functional equa- tion, the quadratic functional equation ...cubic functional equation (.) and the quartic ... See full document

... Hyers-Ulam stability for the Cauchy additive functional inequality and for the Cauchy-Jensen additive functional inequality in the fuzzy normed vector space ... See full document

... and they established the general solution and the Hyers-Ulam stability for the functional equation (.). They proved that a mapping f between two real vector spaces X and Y is a solution of (.) if ... See full document

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

... the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation f x 2y f x − 2y 2f x y 2f − x − y 2fx ... See full document

... the stability of the Cauchy functional equation: a fixed point approach,” in Iteration Theory (ECIT ’02), ...Hyers-Ulam-Rassias stability theorem for a quartic ... See full document

... unique additive mapping A : X → Y, a unique mapping C : X × X × X → Y , and a unique symmetric multi-additive mapping Q : X × X × X × X → Y such that fx Ax Cx, x, x Qx, x, x, x for all x ∈ X, and that C is ... See full document