Stability of some set-valued functional equations

Stability of Quartic Set-valued Functional Equations

We will show the general solution of the functional equation f(x + ay) + f(x− ay) + 2(a − 1)f(x) = af(x + y) + af(x− y) + 2a(a − 1)f(y) and investigate the Hyers-Ulam stability of the quartic set-valued functional equation.

On the stability of fuzzy set-valued functional equations

Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...

On the stability of set-valued functional equations with the fixed point alternative

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic se...

Generalized Orthogonal Stability of Some Functional Equations

We deal with a conditional functional inequality x ⊥ y ⇒ ‖ f (x + y)− f (x)− f (y) ‖ ≤ (‖ x‖ + ‖ y‖ ), where ⊥ is a given orthogonality relation, is a given nonnegative number, and p is a given real number. Under suitable assumptions, we prove that any solution f of the above inequality has to be uniformly close to an orthogonally additive mapping g, that is, satisfying the condition x ⊥ y ⇒ g(...

Stability theorems for some functional differential equations