Superstability of Kannappan s and Van vleck s functional equations

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.