Stability of two functional equations arising from number theory

Generalizing two functional equations introduced in Houston and Sahoo (2008), Jung and Bae (2003), which arise from number theory we prove the stability of the equations f(x1x2+y1y2,x1y2−x2y1)=g(x1,y1)h(x2,y2) for all x1,y1,x2,y2∈Rx1,y1,x2,y2∈R, where f,g,h:R2→Rf,g,h:R2→R, and g(x1,y1,u1,v1)h(x2,y2,u2,v2)=f(x1x2+y1y2+u1u2+v1v2,x1y2−y1x2+u1v2−v1u2,x1u2−y1v2−u1x2+v1y2,x1v2+y1u2−u1y2−v1x2) for all x1,x2,y1,y2,u1,u2,v1,v2∈Rx1,x2,y1,y2,u1,u2,v1,v2∈R, where f,g,h:R4→Rf,g,h:R4→R.