Functional Equation fx pfx − 1 − qfx − 2 and Its Hyers-Ulam Stability
2.Moreover,asubstantialpartofproofofTheorem 2.1canbederivedfromtheoremspresentedinthebooks 19,20 .However,the theorems in 19, 20 deal with solutions of the linear equation under some regularityconditions, for example, the continuity, convexity, diﬀerentiability, analyticity and so on,while Theorem 2.1 deals with the general solution of 1.7 without regularity conditions.
On the Stability of a General Mixed Additive-Cubic Functional Equation in Random Normed Spaces
We prove the generalized Hyers-Ulam stability of the following additive-cubic equation in the setting of random normed spaces.
Hyers-Ulam-Rassias stability of Jensen's equation and its application
The Hyers-Ulam-Rassias stability for the Jensen functional equation is investigated, and the result is applied to the study of an asymptotic behavior of the additive mappings; more precisely, the following asymptotic property shall be proved: Let X and Y be a real normed space and a real Banach space, respectively. A mapping f: X -* Y satisfying f(O) = 0 is additive if and only if 112f [(x + y)/2] f(x) f(y)| -* 0 as llxll + IlYl oo.