On the superstability of the cosine and sine type functional equations

Abstract

In this paper, We study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) and f(xσ(y)a)-f(xya)=2f(x)f(y), where f:S → C is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.

Keywords

• functional equation
• superstablity