Superstability of Kannappan's and Van vleck's functional equations

Abstract

In this paper, we prove the superstability theorems of the functional equations μ(y)f(xσ(y)z0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, μ(y)f(σ(y)xz0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, where S is a semigroup, σ is an involutive morphism of S, and μ : S −→ C is a bounded multiplicative function such that μ(xσ(x)) = 1 for all x ∈ S, and z0 is in the center of S.