Stability of a Generalized Trigonometric-Quadratic Functional Equation

الملخص EN

A stability result for the generalized trigonometric-quadratic functional equation ℱ(x+y)-?(x-y)=2ℋ(x)?(y)+ℒ(x)+ℳ(y) over the domain of a normed space and the range of a Banach space is derived.

It states that under appropriate conditions on the function ℋ(x)?(y), the four functions ℱ(x), ?(x), ℒ(x), and ℳ(x) are approximately equal to combinations of certain quadratic and additive functions.