Abstract

A stability result for the generalized trigonometric-quadratic functional equation ℱ (x + y) - (x - y) = 2 ℋ (x) (y) + (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), (x), and ℳ (x) are approximately equal to combinations of certain quadratic and additive functions. © 2013 Janyarak Tongsomporn and Vichian Laohakosol.