On Stability of Some Types of Functional Equations

Abstract

In this thesis, we study a stability of some types of functional equations. Functional equations are equations in which the unknown (or unknowns) are functions. the aim of this study investigate Hyers-Ulam-Rassias stability of the orthogonally Jensen functional equation in two kinds (additive and quadratic). And study a special case of the Hyers-Ulam stability problem, which is called the superstability. In this study we investigate the superstability of the pexiderized cosine functional equation f1(x + y) + f2(x - y) = 2g1(x)g2(y); where f1; f2; g1 and g2 are functions from R to C: And we get a some critical values of the stability problem, which is a values that is no stability at it. We study the two papers titled “The Stability of the Pexiderized Cosine Functional Equation ˮ by C. Kusollerschariya and P. Nakmahachalasint. [3] and “On the Stability of Orthogonal Functional Equations ˮ by Choonkil Park. [1].